A096401 Number of balanced partitions of n into distinct parts: least part is equal to number of parts.

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 26, 28, 32, 35, 39, 43, 48, 53, 59, 65, 72, 80, 88, 97, 107, 118, 129, 142, 155, 171, 186, 204, 222, 244, 265, 290, 315, 345, 374, 409, 443, 484, 524, 571, 618, 673, 727, 790

Offset

1,12

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Formula

G.f.: Sum_{m>=1} (x^(m*(3*m-1)/2)-x^(m*(3*m+1)/2))/Product_{i=1..m} (1-x^i).

a(n) = A025157(n) - A237979(n) = A237977(n) - A237976(n) for n > 0. - Seiichi Manyama, Jan 13 2022

a(n) ~ (1 - A263719) * A025157(n). - Vaclav Kotesovec, Jan 15 2022

Example

a(14)=3 because we have 12+2, 7+4+3 and 6+5+3.

Maple

G:=sum((x^(m*(3*m-1)/2)-x^(m*(3*m+1)/2))/product(1-x^i, i=1..m), m=1..20): Gser:=series(G, x=0, 80): seq(coeff(Gser, x^n), n=1..78); # Emeric Deutsch, Mar 29 2005

Prog

(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, x^(k*(3*k-1)/2)/prod(j=1, k-1, 1-x^j))) \\ Seiichi Manyama, Jan 15 2022

Crossrefs

Cf. A000009, A025157, A237976, A237977, A237979.

Cf. A006141, A047993, A339446.

Sequence in context: A026829 A025154 A241827 * A264593 A026828 A025153

Adjacent sequences: A096398 A096399 A096400 * A096402 A096403 A096404

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 06 2004

Extensions

More terms from Emeric Deutsch, Mar 29 2005

Status

approved