This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141448 #37 Sep 08 2022 08:45:35
%S A141448 0,1,2,5,13,34,89,232,605,1578,4116,10736,28003,73041,190515,496926,
%T A141448 1296147,3380779,8818187,23000741,59993521,156482896,408159020,
%U A141448 1064613385,2776862948,7242974718,18892067685,49276745441,128530009618
%N A141448 Generalized Pell numbers P(n,5,5).
%C A141448 P(n,2,2) and P(n,2,1) are in A000129.
%C A141448 P(n,3,2) is A116413. P(n,3,1) and P(n,3,3) are A077939.
%C A141448 P(n,4,1) and P(n,4,4) are A103142.
%H A141448 Vincenzo Librandi, <a href="/A141448/b141448.txt">Table of n, a(n) for n = 0..1000</a>
%H A141448 Brian Hopkins and Stéphane Ouvry, <a href="https://arxiv.org/abs/2008.04937">Combinatorics of Multicompositions</a>, arXiv:2008.04937 [math.CO], 2020.
%H A141448 E. Kilic and D. Tasci, <a href="https://doi.org/10.11650/twjm/1500404581">The generalized Binet formula, representation and sums of the generalizedorder-k Pell numbers</a>, Taiwanese J of Math vol 10 no 6 (2006), 1661-1670.
%H A141448 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1,1,1).
%F A141448 From _R. J. Mathar_, Nov 28 2008: (Start)
%F A141448 a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5).
%F A141448 G.f.: x/(1-2*x-x^2-x^3-x^4-x^5). (End)
%F A141448 a(n+1) = Sum_(k=1..n, Sum_(r=0..k, binomial(k,r)*2^(k-r)*Sum_(m=0..r,(Sum_(j=0..m, binomial(j,-r+n-m-k-j)*binomial(m,j)))*binomial(r,m)))), a(0)=0, a(1)=1. [_Vladimir Kruchinin_, May 05 2011]
%p A141448 P := proc(n,k,i) option remember ; if n = 1-i then 1; elif n <= 0 then 0; else 2*P(n-1,k,i)+add(P(n-j,k,i),j=2..k) ; fi ; end: for n from 0 to 40 do printf("%d,",P(n,5,5)) ; od:
%t A141448 CoefficientList[Series[x/(1 - 2*x - x^2 - x^3 - x^4 - x^5), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 13 2012 *)
%t A141448 LinearRecurrence[{2,1,1,1,1},{0,1,2,5,13},40] (* _Harvey P. Dale_, Jan 08 2016 *)
%o A141448 (Maxima)
%o A141448 a(n):=b(n+1);
%o A141448 b(n):=sum(sum(binomial(k,r)*2^(k-r)*sum((sum(binomial(j,-r+n-m-k-j)*binomial(m,j),j,0,m))*binomial(r,m),m,0,r),r,0,k),k,1,n); /* _Vladimir Kruchinin_, May 05 2011 */
%o A141448 (Magma) I:=[0,1,2,5,13]; [n le 5 select I[n] else 2*Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4)+Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Dec 13 2012
%K A141448 nonn,easy
%O A141448 0,3
%A A141448 _R. J. Mathar_, Aug 07 2008