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 A319814 Number of partitions of n into exactly four positive triangular numbers. 6
 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 2, 1, 3, 2, 4, 2, 2, 3, 3, 3, 2, 4, 3, 5, 3, 2, 5, 4, 4, 3, 5, 4, 4, 5, 4, 5, 5, 4, 6, 5, 5, 6, 5, 5, 6, 7, 3, 5, 9, 5, 7, 5, 8, 7, 7, 4, 7, 9, 7, 8, 5, 7, 8, 10, 6, 6, 10, 7, 10, 7, 8, 9, 8, 8, 7, 13, 7, 10, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,10 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..10000 FORMULA a(n) = [x^n y^4] 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 b(n, h(n), 4): seq(a(n), n=4..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], 4]; a /@ Range[4, 120] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *) CROSSREFS Column k=4 of A319797. Cf. A000217. Sequence in context: A228570 A173305 A233867 * A220272 A298917 A322530 Adjacent sequences: A319811 A319812 A319813 * A319815 A319816 A319817 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 28 2018 STATUS approved

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Last modified October 1 14:54 EDT 2023. Contains 365826 sequences. (Running on oeis4.)