A023543 Convolution of natural numbers with A023533.

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

G. C. Greubel, Table of n, a(n) for n = 1..5000

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

Cf. A000027, A023533.

Sequence in context: A185603 A046654 A280724 * A129895 A256212 A360107

Adjacent sequences: A023540 A023541 A023542 * A023544 A023545 A023546

Keyword

nonn

Author

Clark Kimberling

Extensions

Title updated by Sean A. Irvine, Jun 06 2019

Status

approved