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A155001 a(n) = 9*a(n-1) + 72*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=17.

%I A155001 #25 Dec 31 2023 11:36:19
%S A155001 1,1,17,225,3249,45441,642897,9057825,127809009,1802444481,
%T A155001 25424248977,358594243425,5057894117169,71339832581121,
%U A155001 1006226869666257,14192509772837025,200180922571503729,2823489006787799361
%N A155001 a(n) = 9*a(n-1) + 72*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=17.
%C A155001 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 A155001 G. C. Greubel, <a href="/A155001/b155001.txt">Table of n, a(n) for n = 0..850</a>
%H A155001 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,72).
%F A155001 a(n+1) = Sum_{k=0..n} A154929(n,k)*8^(n-k).
%F A155001 G.f.: (1 - 8*x - 64*x^2)/(1 - 9*x - 72*x^2). - _G. C. Greubel_, Apr 20 2021
%p A155001 a[0] := 1: a[1] := 1: a[2] := 17: for n from 3 to 25 do a[n] := 9*a[n-1]+72*a[n-2] end do: seq(a[n], n = 0 .. 17); # _Emeric Deutsch_, Jan 21 2009
%t A155001 LinearRecurrence[{9,72},{1,1,17},20] (* _Harvey P. Dale_, Apr 26 2016 *)
%o A155001 (Magma) I:=[1,17]; [1] cat [n le 2 select I[n] else 9*(Self(n-1) +8*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Apr 20 2021
%o A155001 (Sage)
%o A155001 def A155001_list(prec):
%o A155001     P.<x> = PowerSeriesRing(ZZ, prec)
%o A155001     return P( (1-8*x-64*x^2)/(1-9*x-72*x^2) ).list()
%o A155001 A155001_list(30) # _G. C. Greubel_, Apr 20 2021
%Y A155001 Cf. A154929, A154996, A154997, A154999, A155000.
%K A155001 nonn
%O A155001 0,3
%A A155001 _Philippe Deléham_, Jan 18 2009
%E A155001 Corrected by _Philippe Deléham_, Jan 21 2009
%E A155001 Corrected and extended by _Emeric Deutsch_ and _R. J. Mathar_, Jan 21 2009