A023668 Convolution of A001950 and A023533.

2, 5, 7, 12, 18, 22, 28, 33, 38, 46, 53, 61, 70, 77, 85, 93, 100, 109, 116, 126, 137, 147, 158, 168, 178, 190, 199, 210, 221, 230, 242, 252, 262, 274, 285, 299, 312, 324, 339, 350, 364, 377, 390, 404, 416, 429, 444, 455, 469, 482, 494, 509, 521

Offset

1,1

Links

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

Formula

a(n) = Sum_{j=1..n} A001950(j) * A023533(n-j+1).

T(n, k) = Sum_{j=1..n} A001950(k+1 +binomial(n+2,3) -binomial(j+2,3)), for 0 <= k <= n*(n+3)/2, n >= 1 (as an irregular triangle). - G. C. Greubel, Jul 18 2022

Mathematica

A023668[n_, k_]:= A023668[n, k]= Sum[Floor[(k+1 +Binomial[n+2, 3] -Binomial[j+2, 3])*GoldenRatio^2], {j, n}];
Table[A023668[n, k], {n, 7}, {k, 0, n*(n+3)/2}] (* G. C. Greubel, Jul 18 2022 *)

Prog

(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[Floor(k*(3+Sqrt(5))/2)*A023533(n-k+1): k in [1..n]]): n in [1..80]]; // G. C. Greubel, Jul 18 2022
(SageMath)
def A023668(n, k): return sum( floor((k+1 + binomial(n+2, 3) - binomial(j+2, 3))*golden_ratio^2) for j in (1..n) )
flatten([[A023668(n, k) for k in (0..n*(n+3)/2)] for n in (1..7)]) # G. C. Greubel, Jul 18 2022

Crossrefs

Cf. A001622, A001950, A023533, A023665.

Sequence in context: A320657 A024924 A359339 * A023564 A173088 A005895

Adjacent sequences: A023665 A023666 A023667 * A023669 A023670 A023671

Keyword

nonn

Author

Clark Kimberling

Status

approved