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A023543
Convolution of natural numbers with A023533.
2
1, 2, 3, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 216, 222, 228
OFFSET
1,2
LINKS
FORMULA
From G. C. Greubel, Jul 15 2022: (Start)
a(n) = Sum_{j=1..floor((n+1)/2)} (n - j + 1)*A023533(j).
a(n) = (m+2)*(n+1) - binomial(n+4, 4), for binomial(n+3, 3) - 2 <= m <= binomial(n+4, 3) - 3, and n >= 1, with a(1) = 1, a(2) = 2. (End)
MATHEMATICA
Join[{1, 2}, Table[(m+2)*(n+1) -Binomial[n+4, 4], {n, 6}, {m, Binomial[n+3, 3] -2, Binomial[n+4, 3] -3}]]//Flatten (* G. C. Greubel, Jul 15 2022 *)
PROG
(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[A023533(k)*(n+1-k): k in [1..Floor((n+1)/2)]]): n in [1..100]]; // G. C. Greubel, Jul 15 2022
(SageMath)
[1, 2]+flatten([[(m+2)*(n+1) - binomial(n+4, 4) for m in (binomial(n+3, 3)-2 .. binomial(n+4, 3)-3)] for n in (1..6)]) # G. C. Greubel, Jul 15 2022
CROSSREFS
Sequence in context: A185603 A046654 A280724 * A129895 A256212 A360107
KEYWORD
nonn
EXTENSIONS
Title updated by Sean A. Irvine, Jun 06 2019
STATUS
approved