A023660 Convolution of odd numbers and A023533.

1, 3, 5, 8, 12, 16, 20, 24, 28, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 94, 102, 110, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198, 206, 215, 225, 235, 245, 255, 265, 275, 285, 295, 305, 315, 325, 335, 345, 355, 365, 375, 385, 395, 405

Offset

1,2

Links

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

Formula

From G. C. Greubel, Jul 17 2022: (Start)

a(n) = Sum_{j=0..n-1} (2*j+1)*A023533(n-j).

a(n) = 2*A023543(n-1) + A056556(n).

T(n, k) = (2*k+1)*n + 6*binomial(n+2, 4), for 0 <= k <= n*(n+3)/2 and n >= 1 (as an irregular triangle). (End)

Mathematica

Table[(2*k+1)*n + 6*Binomial[n+2, 4], {n, 7}, {k, 0, n*(n+3)/2}]//Flatten (* G. C. Greubel, Jul 17 2022 *)

Prog

(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[(2*k+1)*A023533(n-k): k in [0..n-1]]): n in [1..80]]; // G. C. Greubel, Jul 17 2022
(SageMath)
def A023660(n, k): return (2*k+1)*n + 6*binomial(n+2, 4)
flatten([[A023660(n, k) for k in (0..n*(n+3)/2)] for n in (1..7)]) # G. C. Greubel, Jul 17 2022

Crossrefs

Cf. A005408, A023533, A023543, A056556.

Sequence in context: A310032 A310033 A289073 * A161339 A023562 A194207

Adjacent sequences: A023657 A023658 A023659 * A023661 A023662 A023663

Keyword

nonn

Author

Clark Kimberling

Status

approved