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A024857 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (Fibonacci numbers). 2

%I #8 Dec 26 2016 12:07:44

%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) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (Fibonacci numbers).

%C Essentially the same as A023864 with different indexing.

%H Harvey P. Dale, <a href="/A024857/b024857.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-1,-1,-3,2,1,1,1).

%F G.f.:(-1-x^5-2*x^2-x)/((x^2+x-1)*(x^4+x^2-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

%t CoefficientList[Series[( (-1-x^5-2x^2-x)/((x^2+x-1)(x^4+x^2-1)^2) ),{x,0,30}],x] (* or *) LinearRecurrence[{1,3,-2,-1,-1,-3,2,1,1,1},{1,2,7,11,27,44,91,147,278,450},30] (* _Harvey P. Dale_, Dec 26 2016 *)

%K nonn

%O 2,2

%A _Clark Kimberling_

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)