A023864 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = (F(2), F(3), F(4), ...), F(n) = Fibonacci(n).

1, 2, 7, 11, 27, 44, 91, 147, 278, 450, 806, 1304, 2257, 3652, 6181, 10001, 16677, 26984, 44551, 72085, 118220, 191284, 312300, 505312, 822513, 1330854, 2161907, 3498039, 5674751, 9181940

Offset

1,2

Comments

Essentially the same as A024857 with different indexing.

Links

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

Formula

Conjecture: G.f.: x*(-1-x^5-2*x^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*Fibonacci[n+2-j], {j, 1, Floor[(n+1)/2]}], {n, 1, 50}] (* G. C. Greubel, Jun 12 2019 *)

Prog

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

Crossrefs

Sequence in context: A023862 A024479 A295138 * A024857 A024481 A024591

Adjacent sequences: A023861 A023862 A023863 * A023865 A023866 A023867

Keyword

nonn

Author

Clark Kimberling

Extensions

Title simplified by Sean A. Irvine, Jun 12 2019

Status

approved