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A023860 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2), t = A000045 (Fibonacci numbers). 1

%I #17 Sep 08 2022 08:44:47

%S 1,1,4,7,17,27,56,91,172,278,498,806,1395,2257,3820,6181,10307,16677,

%T 27534,44551,73064,118220,193012,312300,508341,822513,1336132,2161907,

%U 3507189,5674751,9197732,14882243,24107124,39006146,63159782

%N a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2), t = A000045 (Fibonacci numbers).

%H G. C. Greubel, <a href="/A023860/b023860.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[Sum[j*Fibonacci[n+1-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+1-j)); \\ _G. C. Greubel_, Jun 12 2019

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

%o (Sage) [sum(j*fibonacci(n+1-j) for j in (1..floor((n+1)/2))) for n in (1..50)] # _G. C. Greubel_, Jun 12 2019

%K nonn

%O 1,3

%A _Clark Kimberling_

%E Title simplified, a(15) corrected and more terms from _Sean A. Irvine_, Jun 11 2019

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)