A109765 Expansion of x/((4*x-1)*(2*x-1)*(x+1)).

0, 1, 5, 23, 97, 399, 1617, 6511, 26129, 104687, 419089, 1677039, 6709521, 26840815, 107368721, 429485807, 1717965073, 6871903983, 27487703313, 109950988015, 439804301585, 1759217905391, 7036873019665, 28147494874863

Offset: 0

Author

Creighton Dement, Aug 13 2005

Keywords

• easy
• nonn

Comments

In reference to the program code given, 1baseksumseq[C*D] = A001045 (Jacobsthal sequence, disregard signs).

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

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-2,-8).

Crossrefs

Cf. A001045, A006516, A010036, A006095.

Programs

Mathematica

CoefficientList[Series[x/((4x-1)(2x-1)(x+1)),{x,0,30}],x] (* or *)
LinearRecurrence[{5,-2,-8},{0,1,5},30] (* Harvey P. Dale, Jan 02 2013 *)

Formula

a(n) = 5*a(n-1) - 2*a(n-2) - 8*a(n-3), n >= 3.

a(n) = (1/15)*(6*4^n-5*2^n-(-1)^n).

a(n+1) + a(n) = A006516(n+1).

a(n+2) - a(n) = A010036(n+1).