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A319815
Number of partitions of n into exactly five positive triangular numbers.
5
1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 2, 3, 2, 3, 3, 5, 2, 4, 4, 4, 5, 3, 5, 5, 7, 4, 5, 6, 5, 8, 6, 6, 7, 8, 6, 7, 9, 8, 8, 9, 8, 10, 10, 8, 11, 10, 9, 10, 11, 11, 12, 14, 8, 13, 14, 13, 11, 13, 14, 16, 15, 10, 16, 16, 15, 15, 16, 16, 16, 21, 12, 18
OFFSET
5,10
LINKS
FORMULA
a(n) = [x^n y^5] 1/Product_{j>=1} (1-y*x^A000217(j)).
MAPLE
h:= proc(n) option remember; `if`(n<1, 0,
`if`(issqr(8*n+1), n, h(n-1)))
end:
b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))
end:
a:= n-> b(n, h(n), 5):
seq(a(n), n=5..120);
MATHEMATICA
h[n_] := h[n] = If[n < 1, 0, If[IntegerQ@ Sqrt[8n + 1], n, h[n - 1]]];
b[n_, i_, k_] := b[n, i, k] = If[n==0, If[k==0, 1, 0], If[k > n || i k < n, 0, b[n, h[i - 1], k] + b[n - i, h[Min[n - i, i]], k - 1]]];
a[n_] := b[n, h[n], 5];
a /@ Range[5, 120] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A319797.
Cf. A000217.
Sequence in context: A194314 A006371 A000177 * A373092 A222656 A162545
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 28 2018
STATUS
approved