A024319 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 = (Lucas numbers).

0, 0, 3, 4, 7, 11, 18, 29, 58, 94, 152, 246, 398, 644, 1042, 1686, 2804, 4537, 7341, 11878, 19219, 31097, 50316, 81413, 131729, 213142, 345714, 559377, 905091, 1464468, 2369559, 3834027, 6203586

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)*Lucas(n-j+1). - G. C. Greubel, Jan 19 2022

Mathematica

A023531[n_]:= SquaresR[1, 8n+9]/2;
a[n_]:= Sum[A023531[j]*LucasL[n-j+1], {j, Floor[(n+1)/2]}];
Table[a[n], {n, 40}] (* G. C. Greubel, Jan 19 2022 *)

Prog

(Magma)
A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >;
[ (&+[A023531(j)*Lucas(n-j+1): j in [1..Floor((n+1)/2)]]) : n in [1..40]]; // G. C. Greubel, Jan 19 2022
(Sage)
def A023531(n):
    if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
    else: return 0
[sum( A023531(j)*lucas_number2(n-j+1, 1, -1) for j in (1..floor((n+1)/2)) ) for n in (1..40)] # G. C. Greubel, Jan 19 2022

Crossrefs

Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.

Cf. A000032, A023531.

Sequence in context: A075193 A358995 A042433 * A041209 A293420 A041739

Adjacent sequences: A024316 A024317 A024318 * A024320 A024321 A024322

Keyword

nonn

Author

Clark Kimberling

Status

approved