OFFSET
1,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: Sum_{k>=1} x^(4*k)/Product_{j>=k} (1-x^j). - Seiichi Manyama, May 17 2023
EXAMPLE
a(7) = 3 counts these partitions: 331, 3211, 31111.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i>n, 0, b(n, i+1)+b(n-i, i)))
end:
a:= n-> add(b(n-4*i, i), i=1..n/4):
seq(a(n), n=1..60); # Alois P. Heinz, Mar 03 2014
MATHEMATICA
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 3*Min[p]]], {n, 50}]
(* Second program: *)
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i>n, 0, b[n, i+1] + b[n-i, i]]];
a[n_] := Sum[b[n-4i, i], {i, 1, n/4}];
Array[a, 60] (* Jean-François Alcover, Jun 04 2021, after Alois P. Heinz *)
PROG
(PARI) my(N=50, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/prod(j=k, N, 1-x^j)))) \\ Seiichi Manyama, May 17 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 01 2014
STATUS
approved