A244240 Number of partitions of n into 4 parts such that every i-th smallest part (counted with multiplicity) is different from i.

1, 4, 7, 11, 15, 19, 25, 30, 37, 44, 53, 61, 72, 82, 95, 107, 122, 136, 154, 170, 190, 209, 232, 253, 279, 303, 332, 359, 391, 421, 457, 490, 529, 566, 609, 649, 696, 740, 791, 839, 894, 946, 1006, 1062, 1126, 1187, 1256, 1321, 1395, 1465, 1544, 1619, 1703

Offset

14,2

Links

Alois P. Heinz, Table of n, a(n) for n = 14..1000

Formula

Conjectures from Chai Wah Wu, Apr 18 2024: (Start)

a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10) for n > 26.

G.f.: x^14*(-x^4 + x + 1)*(x^8 - x^5 - 2*x^4 + 2*x + 1)/((x - 1)^4*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)). (End)

G.f.: Sum_{i>2} q^(8+i) * ( q_binomial(3,i) - q^2 - q^3 - Sum_{j=0..i} (q^j) ). - John Tyler Rascoe, Apr 23 2024

Prog

(PARI)
p_q(k) = {prod(j=1, k, 1-q^j); }
GB_q(N, M)= {p_q(N+M)/(p_q(M)*p_q(N)); }
A_q(N) = {my(q='q+O('q^N), g=sum(i=3, N, q^(8+i) * (GB_q(3, i) - q^2 - q^3 - sum(j=0, i, q^j))));
Vec(g)}
A_q(70) \\ John Tyler Rascoe, Apr 23 2024

Crossrefs

Column k=4 of A238406.

Sequence in context: A278452 A056548 A065981 * A310738 A310739 A310740

Adjacent sequences: A244237 A244238 A244239 * A244241 A244242 A244243

Keyword

nonn

Author

Alois P. Heinz, Jun 23 2014

Status

approved