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%I #10 Mar 01 2022 05:32:06
%S 0,0,1,1,3,4,6,11,16,25,39,61,94,147,227,350,546,846,1309,2030,3147,
%T 4875,7558,11715,18154,28136,43609,67586,104747,162346,251610,389958,
%U 604381,936699,1451743,2249991,3487152,5404570,8376292,12982016,20120202,31183350,48329596,74903735
%N Number of compositions (ordered partitions) of n into two or more triangular numbers.
%F a(n) = A023361(n) - A010054(n). - _Alois P. Heinz_, Oct 21 2021
%p b:= proc(n) option remember; `if`(n=0, 1, add(
%p `if`(issqr(8*j+1), b(n-j), 0), j=1..n))
%p end:
%p a:= n-> b(n)-`if`(issqr(8*n+1), 1, 0):
%p seq(a(n), n=0..43); # _Alois P. Heinz_, Oct 21 2021
%t b[n_] := b[n] = If[n == 0, 1, Sum[
%t If[IntegerQ@ Sqrt[8*j + 1], b[n - j], 0], {j, 1, n}]];
%t a[n_] := b[n] - If[IntegerQ@ Sqrt[8*n + 1], 1, 0];
%t Table[a[n], {n, 0, 43}] (* _Jean-François Alcover_, Mar 01 2022, after _Alois P. Heinz_ *)
%Y Cf. A000217, A010054, A023361, A347805, A348526, A348528.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Oct 21 2021