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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). 2

%I

%S 1,2,7,11,27,44,91,147,278,450,806,1304,2257,3652,6181,10001,16677,

%T 26984,44551,72085,118220,191284,312300,505312,822513,1330854,2161907,

%U 3498039,5674751,9181940

%N 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).

%C Essentially the same as A024857 with different indexing.

%H G. C. Greubel, <a href="/A023864/b023864.txt">Table of n, a(n) for n = 1..1000</a>

%F 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

%t Table[Sum[j*Fibonacci[n+2-j], {j,1,Floor[(n+1)/2]}], {n,1,50}] (* _G. C. Greubel_, Jun 12 2019 *)

%o (PARI) a(n) = sum(j=1, floor((n+1)/2), j*fibonacci(n+2-j)); \\ _G. C. Greubel_, Jun 12 2019

%o (MAGMA) [(&+[j*Fibonacci(n+2-j): j in [1..Floor((n+1)/2)]]): n in [1..50]]; // _G. C. Greubel_, Jun 12 2019

%o (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

%K nonn

%O 1,2

%A _Clark Kimberling_

%E Title simplified by _Sean A. Irvine_, Jun 12 2019

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Last modified September 21 21:05 EDT 2021. Contains 347598 sequences. (Running on oeis4.)