|
%I #25 Dec 31 2023 11:36:15
%S 1,1,15,176,2248,27840,348608,4347904,54305280,677924864,8464494592,
%T 105679749120,1319449690112,16473663471616,205678490419200,
%U 2567953077764096,32061620085587968,400298333039493120
%N a(n) = 8*a(n-1) + 56*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=15.
%C The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*a(n-2)), with b some constant. The generating function of these is (1 - b*x - b^2*x^2)/(1 - (b+1)*x - b*(1+b)*x^2). - _R. J. Mathar_, Jan 20 2009
%H G. C. Greubel, <a href="/A155000/b155000.txt">Table of n, a(n) for n = 0..900</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,56).
%F a(n) = Sum_{k=0..n} A155112(n,k)*7^(n-k). - _Philippe Deléham_, Jan 27 2009
%F G.f.: 1 + x*(1+7*x)/(1-8*x-56*x^2). - _Harvey P. Dale_, Dec 11 2012
%p m:=30; S:=series( (1-7*x-49*x^2)/(1-8*x-56*x^2), x, m+1):
%p seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Apr 20 2021
%t Join[{1},LinearRecurrence[{8,56},{1,15},20]] (* _Harvey P. Dale_, Dec 11 2012 *)
%o (Magma) I:=[1,15]; [1] cat [n le 2 select I[n] else 8*(Self(n-1) +7*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Apr 20 2021
%o (Sage)
%o def A155000_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (1-7*x-49*x^2)/(1-8*x-56*x^2) ).list()
%o A155000_list(30) # _G. C. Greubel_, Apr 20 2021
%Y Cf. A154996, A154997, A154999, A155001, A155112.
%K nonn
%O 0,3
%A _Philippe Deléham_, Jan 18 2009
%E More terms from _Philippe Deléham_, Jan 27 2009
|
