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%I #32 Jan 01 2024 11:18:05
%S 0,1,13,158,1911,23105,279344,3377317,40832337,493669894,5968552915,
%T 72160819061,872436565728,10547906344793,127525980259301,
%U 1541810773578190,18640754273664159,225369887048273977
%N a(0)=0, a(1)=1; a(n) = 13*a(n-1) - 11*a(n-2).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-11).
%F a(n) = (1/5)*Sum_{k=0..n} binomial(n, k)*F(5*k) where F(k) denotes the k-th Fibonacci number.
%F G.f.: x / (11*x^2-13*x+1). - _Colin Barker_, Jun 26 2013
%t Join[{a=0,b=1},Table[c=13*b-11*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 21 2011 *)
%o (PARI) a(n)=(1/5)*sum(k=0,n,binomial(n,k)*fibonacci(5*k));
%o (Sage) [lucas_number1(n,13,11) for n in range(0, 18)] # _Zerinvary Lajos_, Apr 29 2009
%Y Cf. A030191.
%K nonn,easy
%O 0,3
%A _Benoit Cloitre_, Jun 21 2003