|
%I #23 Jan 01 2024 11:37:41
%S 0,1,8,29,128,537,2280,9653,40896,173233,733832,3108557,13168064,
%T 55780809,236291304,1000946021,4240075392,17961247585,76085065736,
%U 322301510525,1365291107840,5783465941881,24499154875368
%N a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 8.
%C A048878(n) = a(n) + a(n+1). Compare with A110526.
%H G. C. Greubel, <a href="/A110527/b110527.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,1).
%F G.f.: -x*(1+5*x)/((1+x)*(x^2+4*x-1)).
%F a(n) = (-1)^n + 3*A001076(n) - A015448(n). - _Ehren Metcalfe_, Nov 18 2017
%p seriestolist(series(-x*(1+5*x)/((1+x)*(x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1lesseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')], apart from initial term.
%t LinearRecurrence[{3,5,1},{0,1,8},30] (* _Harvey P. Dale_, Feb 12 2015 *)
%o (PARI) x='x+O('x^50); concat(0, Vec(-x*(1+5*x)/((1+x)*(x^2+4*x-1)))) \\ _G. C. Greubel_, Aug 30 2017
%Y Cf. A110526, A110528, A033887, A001076, A049661, A033887.
%K easy,nonn
%O 0,3
%A _Creighton Dement_, Jul 24 2005
|
