A107852 Expansion of -x*(x^2+1)*(x+1)^2/((2*x^3+x^2-1)*(x^4+1)).

0, 1, 2, 3, 6, 7, 10, 17, 22, 37, 58, 83, 134, 199, 298, 465, 694, 1061, 1626, 2451, 3750, 5703, 8650, 13201, 20054, 30501, 46458, 70611, 107462, 163527, 248682, 378449, 575734, 875813, 1332634, 2027283, 3084262, 4692551, 7138826, 10861073

Offset

0,3

Comments

Floretion Algebra Multiplication Program, FAMP Code: 1baseiforzapseq[(.5i' + .5j' + .5'ki' + .5'kj')*(.5'i + .5'j + .5'ik' + .5'jk')], 1vesforzap = A000004

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,2,-1,0,1,2).

Formula

a(n) = 2*A159284(n) - A091337(n).

a(n) = a(n-2) + 2*a(n-3) - a(n-4) + a(n-6) + 2*a(n-7) for n>6. - Colin Barker, Apr 30 2019

Mathematica

CoefficientList[Series[-x(x^2+1)(x+1)^2/((2x^3+x^2-1)(x^4+1)), {x, 0, 50}], x] (* or *) LinearRecurrence[ {0, 1, 2, -1, 0, 1, 2}, {0, 1, 2, 3, 6, 7, 10}, 50] (* Harvey P. Dale, May 03 2024 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 2, 1, 0, -1, 2, 1, 0]^n*[0; 1; 2; 3; 6; 7; 10])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
(PARI) concat(0, Vec(x*(1 + x)^2*(1 + x^2) / ((1 - x^2 - 2*x^3)*(1 + x^4)) + O(x^45))) \\ Colin Barker, Apr 30 2019

Crossrefs

Cf. A107849, A107850, A107851, A107853.

Sequence in context: A051733 A058632 A086583 * A362286 A050031 A003421

Adjacent sequences: A107849 A107850 A107851 * A107853 A107854 A107855

Keyword

easy,nonn

Author

Creighton Dement, May 25 2005

Status

approved