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

Author

Clark Kimberling

Keywords

• nonn

Links

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

Programs

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

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 *)

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

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

Extensions

Title simplified by Sean A. Irvine, Jun 12 2019