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A189732 a(1)=1, a(2)=5, a(n) = a(n-1) + 5*a(n-2).

%I A189732 #41 Dec 31 2023 10:23:06
%S A189732 1,5,10,35,85,260,685,1985,5410,15335,42385,119060,330985,926285,
%T A189732 2581210,7212635,20118685,56181860,156775285,437684585,1221561010,
%U A189732 3409983935,9517788985,26567708660,74156653585,206995196885,577778464810,1612754449235,4501646773285
%N A189732 a(1)=1,  a(2)=5, a(n) = a(n-1) + 5*a(n-2).
%H A189732 Vincenzo Librandi, <a href="/A189732/b189732.txt">Table of n, a(n) for n = 1..100</a>
%H A189732 Silvana Ramaj, <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=3464&amp;context=etd">New Results on Cyclic Compositions and Multicompositions</a>, Master's Thesis, Georgia Southern Univ., 2021. See p. 33.
%H A189732 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 5).
%F A189732 G.f.: x*(1+4*x)/(1-x-5*x^2). - _Bruno Berselli_, May 24 2011
%F A189732 a(n+1) = Sum_{k=0..n} A119473(n,k)*4^k. - _Philippe Deléham_, Oct 05 2012
%t A189732 LinearRecurrence[{1,5},{1,5},40]
%o A189732 (Maxima) a[1]:1$ a[2]:5$ a[n]:=a[n-1]+5*a[n-2]$ makelist(a[n], n, 1, 29);  /* _Bruno Berselli_, May 24 2011 */
%o A189732 (PARI) a(n)=([0,1; 5,1]^(n-1)*[1;5])[1,1] \\ _Charles R Greathouse IV_, Oct 21 2022
%Y A189732 Cf. A000045, A000079, A105476, A159612, A080040, A135522, A103435, A189734, A189735, A189736, A189737, A189738, A189739, A189741, A189742, A189743, A189744, A189745, A189746, A189747, A189748, A189749.
%K A189732 nonn,easy
%O A189732 1,2
%A A189732 _Harvey P. Dale_, Apr 26 2011