cp's OEIS Frontend

A113254 Corresponds to m = 8 in a family of 4th-order linear recurrence sequences given by a(m,n) = m^4*a(n-4) + (2*m)^2*a(n-3) - 4*a(m-1), a(m,0) = -1, a(m,1) = 4, a(m,2) = -13 + 6*(m-1) + 3*(m-1)^2, a(m,3) = (-8+m^2)^2.

%I A113254 #13 Jun 10 2024 16:08:34
%S A113254 -1,4,176,3136,-15616,123904,1028096,4734976,-51183616,975437824,
%T A113254 1521483776,205520896,39241908224,4227925540864,-10627091267584,
%U A113254 53396107165696,1029499365883904,10479050187341824,-71775363146973184,769363745204862976
%N A113254 Corresponds to m = 8 in a family of 4th-order linear recurrence sequences given by a(m,n) = m^4*a(n-4) + (2*m)^2*a(n-3) - 4*a(m-1), a(m,0) = -1, a(m,1) = 4, a(m,2) = -13 + 6*(m-1) + 3*(m-1)^2, a(m,3) = (-8+m^2)^2.
%C A113254 Conjecture: a(m, 2*n+1) is a perfect square for all m,n (see A113249).
%H A113254 Colin Barker, <a href="/A113254/b113254.txt">Table of n, a(n) for n = 0..1000</a>
%H A113254 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,0,256,4096).
%F A113254 G.f.: (-1+192*x^2+4096*x^3) / ((8*x+1)*(1-8*x)*(64*x^2+4*x+1)).
%F A113254 a(n) = -4*a(n-1) + 256*a(n-3) + 4096*a(n-4) for n > 3. - _Colin Barker_, May 20 2019
%t A113254 LinearRecurrence[{-4, 0, 256, 4096}, {-1, 4, 176, 3136}, 25] (* _Paolo Xausa_, Jun 10 2024 *)
%o A113254 (PARI) Vec(-(1 - 192*x^2 - 4096*x^3) / ((1 - 8*x)*(1 + 8*x)*(1 + 4*x + 64*x^2)) + O(x^25)) \\ _Colin Barker_, May 20 2019
%Y A113254 Cf. A000302, A097948, A056450, A113249, A113250, A113251, A113252, A113253, A113255, A113256.
%K A113254 easy,sign
%O A113254 0,2
%A A113254 _Creighton Dement_, Nov 18 2005