A023866 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t is A000201 (lower Wythoff sequence).

1, 3, 10, 14, 32, 43, 77, 93, 147, 169, 248, 283, 393, 437, 582, 644, 829, 903, 1133, 1219, 1498, 1608, 1942, 2067, 2460, 2601, 3058, 3230, 3756, 3946, 4546, 4772, 5451, 5699, 6462, 6732, 7583, 7895, 8840, 9177, 10220, 10604, 11750, 12162, 13416, 13856, 15223, 15717

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

Table[Sum[j*Floor[(n+1-j)*GoldenRatio], {j, 1, Floor[(n+1)/2]}], {n, 1, 50}] (* G. C. Greubel, Jun 12 2019 *)

Prog

(PARI) {a(n) = sum(j=1, floor((n+1)/2), j*floor((n+1-j)*(1+sqrt(5))/2))}; \\ G. C. Greubel, Jun 12 2019
(Magma) [(&+[j*Floor((n+1-j)*(1+Sqrt(5))/2): j in [1..Floor((n+1)/2)]]): n in [1..50]]; // G. C. Greubel, Jun 12 2019
(Sage) [sum(j*floor((n+1-j)*golden_ratio) for j in (1..floor((n+1)/2))) for n in (1..50)] # G. C. Greubel, Jun 12 2019

Crossrefs

Sequence in context: A063221 A022409 A245524 * A024593 A128930 A328091

Adjacent sequences: A023863 A023864 A023865 * A023867 A023868 A023869

Keyword

nonn

Author

Clark Kimberling

Extensions

Title simplified by Sean A. Irvine, Jun 12 2019

Status

approved