|
%I #8 Jul 31 2015 18:01:45
%S 1,4,25,119,599,2887,14039,67767,327607,1581751,7638967,36883895,
%T 178097591,859930039,4152135095,20048276919,96801746359,467400158647,
%U 2256808013239,10896832949687,52614565424567,254045594545591
%N Expansion of (1-x+2*x^3+x^2)/((1-x)*(2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, 4, -24, 0, 16).
%F a(0)=1, a(1)=4, a(2)=25, a(3)=119, a(4)=599, a(n)=5*a(n-1)+4*a(n-2)- 24*a(n-3)+ 16*a(n-5). - _Harvey P. Dale_, Sep 07 2012
%F a(n)=1/112*(-2*(7*(-2)^n+7*2^(n+1)-8)+(13-9*Sqrt[2])*(2-2*Sqrt[2])^n+ 9* 2^(n+1/2)*(1+Sqrt[2])^n+13*(2*(1+Sqrt[2]))^n). - _Harvey P. Dale_, Sep 07 2012
%p seriestolist(series((1-x+2*x^3+x^2)/((1-x)*(2*x+1)*(2*x-1)*(4*x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -basejrokseq[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'; RokType: Y[15] = Y[15] + 1/2
%t CoefficientList[Series[(1-x+2x^3+x^2)/((1-x)(2x+1) (2x-1) (4x^2+4x-1)), {x,0,30}],x] (* or *) LinearRecurrence[{5,4,-24,0,16},{1,4,25,119,599},30] (* _Harvey P. Dale_, Sep 07 2012 *)
%Y Cf. A110050, A110052.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Jul 10 2005
|
