A024325 a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = A001950 (upper Wythoff sequence).
0, 0, 5, 7, 10, 13, 15, 18, 33, 38, 44, 48, 54, 60, 64, 70, 98, 106, 114, 121, 130, 137, 145, 153, 160, 169, 213, 223, 233, 244, 255, 265, 275, 286, 297, 307, 317, 328, 391, 403, 416, 430, 442, 456, 469, 481, 496, 508, 521, 534, 547, 561, 644, 659, 675, 690, 707, 722, 737, 755
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
-
Magma
A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >; A024325:= func< n | (&+[A023531(j)*Floor((n-j+1)*(3+Sqrt(5))/2): j in [1..Floor((n+1)/2)]]) >; [A024325(n) : n in [1..80]]; // G. C. Greubel, Jan 28 2022
-
Mathematica
A023531[n_] := SquaresR[1, 8n+9]/2; a[n_]:= a[n]= Sum[A023531[j]*Floor[(n-j+1)*GoldenRatio^2], {j,Floor[(n+1)/2]}]; Table[a[n], {n, 80}] (* G. C. Greubel, Jan 28 2022 *)
-
Sage
def A023531(n): if ((sqrt(8*n+9) -3)/2).is_integer(): return 1 else: return 0 def A023325(n): return sum( A023531(j)*floor(((n-j+1)*(3+sqrt(5)))/2) for j in (1..((n+1)//2)) ) [A023325(n) for n in (1..80)] # G. C. Greubel, Jan 28 2022
Comments