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A103142 a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=1, a(1)=2, a(3)=5, a(4)=13.

%I A103142 #57 Sep 08 2022 08:45:16
%S A103142 1,2,5,13,34,88,228,591,1532,3971,10293,26680,69156,179256,464641,
%T A103142 1204374,3121801,8091873,20974562,54367172,140922580,365278767,
%U A103142 946821848,2454212215,6361447625,16489208080,42740897848,110786663616,287164880785,744346531114
%N A103142 a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=1, a(1)=2, a(3)=5, a(4)=13.
%C A103142 Row sums of generalized Pascal matrix A103141.
%C A103142 Generalized Pell numbers.
%C A103142 Row sums of the tetranacci convolution triangle A202193. - _Philippe Deléham_, Feb 16 2014
%H A103142 Vincenzo Librandi, <a href="/A103142/b103142.txt">Table of n, a(n) for n = 0..500</a>
%H A103142 Brian Hopkins and Stéphane Ouvry, <a href="https://arxiv.org/abs/2008.04937">Combinatorics of Multicompositions</a>, arXiv:2008.04937 [math.CO], 2020.
%H A103142 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1,1).
%F A103142 a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4).
%F A103142 G.f.: 1/(1 - 2*x - x^2 - x^3 - x^4).
%p A103142 m:=40; S:=series(1/(1-2*x-x^2-x^3-x^4), x, m+1): seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Feb 12 2020
%t A103142 LinearRecurrence[{2,1,1,1}, {1,2,5,13}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Jun 20 2011 *)
%o A103142 (PARI) Vec(1/(1-2*x-x^2-x^3-x^4)+O(x^40)) \\ _Charles R Greathouse IV_, Jun 20 2011
%o A103142 (Magma) I:=[1,2,5,13]; [n le 4 select I[n] else 2*Self(n-1)+Self(n-2)+Self(n-3) +Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Feb 05 2012
%o A103142 (Sage)
%o A103142 def A103142_list(prec):
%o A103142     P.<x> = PowerSeriesRing(ZZ, prec)
%o A103142     return P( 1/(1-2*x-x^2-x^3-x^4) ).list()
%o A103142 A103142_list(40) # _G. C. Greubel_, Feb 12 2020
%o A103142 (GAP) a:=[1,2,5,13];; for n in [5..40] do a[n]:=2*a[n-1]+a[n-2]+a[n-3]+a[n-4]; od; a; # _G. C. Greubel_, Feb 12 2020
%Y A103142 Cf. A000129, A077939.
%Y A103142 Row sums of A103141 and of A202193.
%K A103142 easy,nonn
%O A103142 0,2
%A A103142 _Paul Barry_, Jan 24 2005
%E A103142 Deleted certain dangerous or potentially dangerous links. - _N. J. A. Sloane_, Jan 30 2021