A023867 a(n) = 1*t(n) + 2*t(n-1) + ...+ k*t(n+1-k), where k=floor((n+1)/2) and t is A001950 (upper Wythoff sequence).

2, 5, 17, 24, 54, 71, 127, 153, 242, 279, 409, 465, 645, 717, 954, 1052, 1354, 1473, 1848, 1989, 2444, 2620, 3164, 3367, 4007, 4239, 4983, 5260, 6116, 6426, 7402, 7764, 8868, 9269, 10509, 10950, 12333, 12835, 14370, 14917, 16611, 17226, 19087, 19752, 21788, 22504

Offset

1,1

Links

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A023244 A188535 A176582 * A024594 A106215 A211548

Adjacent sequences: A023864 A023865 A023866 * A023868 A023869 A023870

Keyword

nonn

Author

Clark Kimberling

Extensions

Title simplified by Sean A. Irvine, Jun 12 2019

Status

approved