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A244240
Number of partitions of n into 4 parts such that every i-th smallest part (counted with multiplicity) is different from i.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 23 2014
STATUS
approved