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

1,3

Links

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

Formula

a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A001950(n-j+1).

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 *)

Prog

(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
(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

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024326, A024327.

Cf. A001950, A023531.

Sequence in context: A243187 A333308 A179196 * A060873 A186542 A287444

Adjacent sequences: A024322 A024323 A024324 * A024326 A024327 A024328

Keyword

nonn

Author

Clark Kimberling

Status

approved