|
%I #14 Mar 11 2023 08:37:45
%S 1,61,4621,369181,29821741,2414250301,195533302861,15837861987421,
%T 1282861452271981,103911691734684541,8416845656119913101,
%U 681764476155480405661,55222922216750191970221
%N Sum of odd powers of 4 and 9 divided by 13.
%H G. C. Greubel, <a href="/A165259/b165259.txt">Table of n, a(n) for n = 0..520</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (97,-1296).
%F G.f.: (1-36*x)/((1-16*x)*(1-81*x))
%F a(n) = 97*a(n-1) - 1296*a(n-2). - _Harvey P. Dale_, Jun 23 2013
%F E.g.f.: (1/13)*(4*exp(16*x) + 9*exp(81*x)). - _G. C. Greubel_, Mar 11 2023
%t Table[(4^n+9^n)/13,{n,1,31,2}] (* or *) LinearRecurrence[{97,-1296},{1,61},20] (* _Harvey P. Dale_, Jun 23 2013 *)
%o (PARI) a(n)=(4^(2*n+1)+9^(2*n+1))/13
%o (Magma) [(4^(2*n+1)+9^(2*n+1))/13: n in [0..30]]; // _G. C. Greubel_, Mar 11 2023
%o (SageMath) [(4^(2*n+1)+9^(2*n+1))/13 for n in range(31)] # _G. C. Greubel_, Mar 11 2023
%Y Cf. A007689, A082101, A096951.
%K nonn
%O 0,2
%A _Jaume Oliver Lafont_, Sep 11 2009
| 