A023861 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = A000032 (Lucas numbers).

1, 3, 10, 15, 37, 61, 126, 203, 384, 622, 1114, 1802, 3119, 5047, 8542, 13821, 23047, 37291, 61568, 99619, 163376, 264348, 431588, 698324, 1136685, 1839195, 2987682, 4834171, 7842313, 12689129, 20566754, 33277707, 53905168, 87220394, 141229566, 228514238, 369921435

Offset

1,2

Links

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

Formula

Conjecture: G.f.: x*(-1-3*x^5+x^4+2*x^3-4*x^2-2*x)/((x^2+x-1)* (x^4+x^2-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

Mathematica

Table[Sum[j*LucasL[n+1-j], {j, 1, Floor[(n+1)/2]}], {n, 1, 50}] (* G. C. Greubel, Jun 12 2019 *)

Prog

(PARI) lucas(n) = fibonacci(n-1)+fibonacci(n+1);
a(n) = sum(j=1, floor((n+1)/2), j*lucas(n+1-j)); \\ G. C. Greubel, Jun 12 2019
(Magma) [(&+[j*Lucas(n+1-j): j in [1..Floor((n+1)/2)]]): n in [1..50]]; // G. C. Greubel, Jun 12 2019
(Sage) [sum(j*lucas_number2(n+1-j, 1, -1) for j in (1..floor((n+1)/2))) for n in (1..50)] # G. C. Greubel, Jun 12 2019

Crossrefs

Sequence in context: A330940 A351010 A020330 * A037345 A217278 A175336

Adjacent sequences: A023858 A023859 A023860 * A023862 A023863 A023864

Keyword

nonn

Author

Clark Kimberling

Extensions

Title simplified by Sean A. Irvine, Jun 12 2019

Terms a(30) onward added by G. C. Greubel, Jun 12 2019

Status

approved