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%I #17 Mar 12 2024 14:51:33
%S 0,1,5,23,97,399,1617,6511,26129,104687,419089,1677039,6709521,
%T 26840815,107368721,429485807,1717965073,6871903983,27487703313,
%U 109950988015,439804301585,1759217905391,7036873019665,28147494874863
%N Expansion of x/((4*x-1)*(2*x-1)*(x+1)).
%C In reference to the program code given, 1baseksumseq[C*D] = A001045 (Jacobsthal sequence, disregard signs).
%C Floretion Algebra Multiplication Program, FAMP Code: 1basejsumseq[C*D] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' and D = + .5'i + .5'k - .5j' - .5k' + .5'ii' + .5'jj' + .5'jk' + .5'ki'; sumtype: sum[Y[15]] = sum[Y[ * ]], disregard signs
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-2,-8).
%F a(n) = 5*a(n-1) - 2*a(n-2) - 8*a(n-3), n >= 3.
%F a(n) = (1/15)*(6*4^n-5*2^n-(-1)^n).
%F a(n+1) + a(n) = A006516(n+1).
%F a(n+2) - a(n) = A010036(n+1).
%t CoefficientList[Series[x/((4x-1)(2x-1)(x+1)),{x,0,30}],x] (* or *)
%t LinearRecurrence[{5,-2,-8},{0,1,5},30] (* _Harvey P. Dale_, Jan 02 2013 *)
%Y Cf. A001045, A006516, A010036, A006095.
%K easy,nonn
%O 0,3
%A _Creighton Dement_, Aug 13 2005