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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).
17
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
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
KEYWORD
nonn
STATUS
approved