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 A224679 Number of compositions of n^2 into sums of positive triangular numbers. 4
 1, 1, 3, 25, 546, 28136, 3487153, 1038115443, 742336894991, 1275079195875471, 5260826667789867957, 52137661179700350278531, 1241165848412448464485760897, 70972288312605764017275784402928, 9748291749334923037419108242002717050 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..72 FORMULA a(n) = A023361(n^2), where A023361(n) = number of compositions of n into positive triangular numbers. a(n) = [x^(n^2)] 1/(1 - Sum_{k>=1} x^(k*(k+1)/2)). MAPLE b:= proc(n) option remember; local i; if n=0 then 1 else 0; for i while i*(i+1)/2<=n do %+b(n-i*(i+1)/2) od; % fi end: a:= n-> b(n^2): seq(a(n), n=0..20); # Alois P. Heinz, Feb 05 2018 MATHEMATICA b[n_] := b[n] = Module[{i, j = If[n == 0, 1, 0]}, For[i = 1, i(i+1)/2 <= n, i++, j += b[n-i(i+1)/2]]; j]; a[n_] := b[n^2]; a /@ Range[0, 20] (* Jean-François Alcover, Nov 04 2020, after Alois P. Heinz *) PROG (PARI) {a(n)=polcoeff(1/(1-sum(r=1, n+1, x^(r*(r+1)/2)+x*O(x^(n^2)))), n^2)} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A023361, A224366, A224677. Sequence in context: A243440 A306783 A003024 * A213599 A179473 A248417 Adjacent sequences: A224676 A224677 A224678 * A224680 A224681 A224682 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 14 2013 STATUS approved

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Last modified December 4 16:44 EST 2023. Contains 367563 sequences. (Running on oeis4.)