Sequences

Initial members of prime octuplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26).

Initial members of prime octuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26).

Initial members of prime octuplets (p, p+6, p+8, p+14, p+18, p+20, p+24, p+26).

Tri-substituted alkanes of form C_n H_{2n-1} X_2 Y, or equivalently bi-substituted alkyls of form -C_n H_{2n-1} X_2 (n=1: CHXXY; n=2: CXXY-CHHH CXYH-CXHH CXXH-CYHH).

a(n)=2a(n-1)+3a(n-2)+2a(n-3)+3a(n-4).

Number of partially ordered sets with no isolated points and with n "lines": pairs (a,b) where a < b and there is no c with a < c < b. The lines form the minimal basis for the partial ordering.

Number of connected partially ordered sets with n "lines": pairs (a,b) where a < b and there is no c with a < c < b. The lines form the minimal basis for the partial ordering.

Define the sequence UD(a(0),a(1)) by a(n) is the least integer such that a(n)/a(n-1) > a(n-1)/a(n-2)+1 for even n >= 2 and such that a(n)/a(n-1) > a(n-1)/a(n-2) for odd n>=2. This is UD(2,16).

Define the sequence S(a(0), a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0 . This is S(2,32).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(3,9).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(5,20).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(5,45).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(6,30).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(6,66).

Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(6,102).

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(2,15).

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(2,16).

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(2,32).

a(n) = 3*a(n-1) + a(n-2) - a(n-3) - a(n-5).

For even n, a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n); for odd n, the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n); a(0) = 4, a(1) = 16.

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(4,17).

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(5,26).

Expansion of 1/((1-x)(1-5x)(1-6x)(1-7x)).

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(6,31).

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(6,37).

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(7,43).

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(7,50).

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(8,57).

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(8,65).

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(16,36).

a(n) = 3*a(n-1)+a(n-2)-a(n-3)+a(n-6)-a(n-7)+a(n-10)-a(n-11).

Theta series of D_11 lattice.

Theta series of D_12 lattice.

Theta series of D_13 lattice.

Theta series of D_14 lattice.

Theta series of D_15 lattice.

Theta series of D_16 lattice.

Theta series of D_17 lattice.

Theta series of D_18 lattice.

Theta series of D_19 lattice.

Theta series of D_20 lattice.

Theta series of D_21 lattice.

Theta series of D_22 lattice.

Theta series of D_23 lattice.

Theta series of D_24 lattice.

Theta series of D_25 lattice.

Theta series of D_26 lattice.

Theta series of D_27 lattice.

Theta series of D_28 lattice.

Theta series of D_29 lattice.