Sequences

Number of ways of making change for n cents using coins of 1, 2, 4, 10, 20, 40, 100 cents.

Final 2 digits of 6^n.

Number of ways of making change for n cents using coins of 1, 2, 5, 10, 50, 100 cents.

Number of ways of making change for n cents using coins of 1, 2, 5, 10, 20, 50 cents.

Number of (unordered) ways of making change for n cents using coins of 2, 5 (two kinds), 10, 20, 50 cents.

a(n) = Sum_{k=0..n} 2^binomial(n,k).

Gould's sequence: a(n) = Sum_{k=0..n} (binomial(n,k) mod 2); number of odd entries in row n of Pascal's triangle (A007318); a(n) = 2^A000120(n).

Sierpiński's triangle (Pascal's triangle mod 2) converted to decimal.

Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....

Number of (unordered) ways of making change for n cents using coins of 2, 5, 10, 20, 50 cents.

Number of self-complementary Boolean functions of n variables, up to equivalence under the group (C_2)^n of all 2^n complementations of variables.

Number of equivalence classes of 3-valued Post functions of n variables under action of symmetric group S_n.

Number of equivalence classes of n-valued Post functions of 2 variables under action of symmetric group S_2.

Number of equivalence classes of 3-valued Post functions of n variables under action of semi-direct product of symmetric group S_n and complementing group C(n,3).

Number of equivalence classes of n-valued Post functions of 2 variables under action of semi-direct product of symmetric group S_2 and complementing group C(2,n).

Number of equivalence classes of 3-valued Post functions of n variables under action of semi-direct product of symmetric group S_n and complementing group D(n,3).

Number of equivalence classes of n-valued Post functions of 2 variables under action of semi-direct product of symmetric group S_2 and complementing group D(2,n).

Number of equivalence classes of 3-valued Post functions of n variables under action of semi-direct product of symmetric groups S_n and S(n,3).

Number of equivalence classes of n-valued Post functions of 2 variables under action of semi-direct product of symmetric groups S_2 and S(2,n).

Number of nonisomorphic groupoids with n elements.

Number of n-element algebras with 2 binary operations.

Number of n-element algebras with 1 ternary operation.

a(n) = Bernoulli(2*n) * (2*n + 1)!.

Pell-Lucas numbers: numerators of continued fraction convergents to sqrt(2).

Number of n-step self-avoiding walks on hexagonal [ =triangular ] lattice.

Number of n-step polygons on hexagonal lattice.

Number of n-step self-avoiding walks on f.c.c. lattice.

Number of n-step polygons on f.c.c. lattice.

-1 + Sum (k-1)! C(n,k), k = 1..n for n > 0, a(0) = 1.

a(n) = Sum_{k=0..n} (k+1)! binomial(n,k).

E.g.f.: 2*exp(x)/(1-x)^3.

Expansion of e.g.f. 6*exp(x)/(1-x)^4.

E.g.f.: 24*exp(x)/(1-x)^5.

Number of (unordered) ways of making change for n cents using coins of 5, 10, 20, 50, 100 cents.

a(n) = Sum_{k=0..2} (n+k)! * C(2,k).

a(n) = Sum_{k = 0..3} (n+k)! C(3,k).

a(n) = Sum_{k = 0..4} (n+k)! C(4,k).

a(n) = Sum_{k=0..5} (n+k)! * C(5,k).

Mersenne numbers: 2^p - 1, where p is prime.

Number of simple connected graphs on n unlabeled nodes.

Associated Mersenne numbers.

Associated Mersenne numbers.

a(0) = 1, a(1) = 6, a(2) = 24; for n>=3, a(n) = 4a(n-1) - a(n-2).

a(n) = 4*a(n-1) - a(n-2) with a(0) = 0, a(1) = 1.

Coordination sequence for hyperbolic tessellation 3^7 (from triangle group (2,3,7)).

Mix digits of Pi and e.

Dates at fortnightly intervals from Jan 01 in the Julian calendar.

Powers of 2 written in base 9.

Semiprimes (or biprimes): products of two primes.

Lesser of twin primes.