Sequences

Expansion of 1/((1-4x)(1-5x)(1-9x)).

Expansion of 1/((1-4x)(1-5x)(1-10x)).

a(n) = 9*a(n - 1) - a(n - 2) for n>1, a(0)=0, a(1)=1.

Pisot sequence T(2,5), a(n) = floor(a(n-1)^2/a(n-2)).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(2,6).

Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(2,8).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(3,5).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(3,6).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(3,9).

Pisot sequence T(3,10), a(n) = floor(a(n-1)^2/a(n-2)).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(4,8).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(8,16).

Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(16,32).

Number of isotropic subspaces of an n-dimensional symplectic space over GF(4).

Number of isotropic subspaces of a 2n-dimensional unitary space over GF(4).

Number of ways to partition an n-cube into subcubes (without reducing isomorphic cases); number of labeled squashed n-cubes; ways to make a tautology from disjoint terms with n Boolean variables; number of Rivest compression schemes for n-bit retrieval.

For each permutation p of {1,2,...,n} define maxjump(p) = max(p(i) - i); a(n) is sum of maxjumps of all p.

Define {b(n)} by b(1)=3, b(n) (n >= 2) is the smallest number such that b(1)^2 + ... + b(n)^2 = m^2 for some m and all b(i) are distinct. Sequence gives values of m.

Define {b(n)} by b(1) = 3, b(n) (n >= 2) is smallest number such that b(1)^2 + ... + b(n)^2 = m^2 for some m and all b(i) are distinct. Sequence gives values of m^2.

a(1)=3; for n>1, a(n) is smallest positive integer such that a(1)^2+...+a(n)^2 = m^2 for some m.

The number of permutations of n cards in which 2 is the first card hit and 3 the next hit after 2.

The number of permutations of n cards in which 4 will be the next hit after 2.

From the game of Mousetrap.

From the game of Mousetrap.

a(n) is the smallest m whose square is the sum of n distinct positive squares.

a(n) is the smallest square that is the sum of n distinct positive squares.

Let S be the smallest square that is the sum of n distinct positive integers. Then a(n) is the smallest k such that there exist n distinct positive integers <= k whose squares sum to S.

Decimal expansion of e^Pi - Pi.

Continued fraction for e^Pi - Pi.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite ABW = Li-A (Barrer and White).

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AEI = AlPO4-18 [Al24P24O96] starting with a T1 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AEI = AlPO4-18 [Al24P24O96] starting with a T2 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AEI = AlPO4-18 [Al24P24O96] starting with a T3 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AEL = AlPO4-11 [Al20P20O80] starting with a T3 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AEL = AlPO4-11 [Al20P20O80] starting with a T1 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AEL = AlPO4-11 [Al20P20O80] starting with a T2 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AET = AlPO4-8 [Al36P36O144] starting with a T4 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AET = AlPO4-8 [Al36P36O144] starting with a T1 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AET = AlPO4-8 [Al36P36O144] starting with a T3 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AET = AlPO4-8 [Al36P36O144] starting with a T2 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AET = AlPO4-8 [Al36P36O144] starting with a T5 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFG = Afghanite (Na2,Ca,K2)12[Al24Si24O96] starting with a T1 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFG = Afghanite (Na2,Ca,K2)12[Al24Si24O96] starting with a T2 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFG = Afghanite (Na2,Ca,K2)12[Al24Si24O96] starting with a T3 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFI = AlPO4-5 [ Al12P12O48 ] . R . q H2O.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFO = AlPO4-41 [Al20P20O80] starting with a T4 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFO = AlPO4-41 [Al20P20O80] starting with a T3 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFO = AlPO4-41 [Al20P20O80] starting with a T2 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFO = AlPO4-41 [Al20P20O80] starting with a T1 atom.

Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for zeolite AFR = SAPO-40 [Si7Al29P28O128].4TPA.OH starting with a T1 atom.