A107851 Expansion of g.f. x*(-1-x-3*x^2-x^3+2*x^5)/((2*x^3+x^2-1)*(x^4+1)).

0, 1, 1, 4, 4, 5, 9, 10, 18, 29, 41, 68, 100, 149, 233, 346, 530, 813, 1225, 1876, 2852, 4325, 6601, 10026, 15250, 23229, 35305, 53732, 81764, 124341, 189225, 287866, 437906, 666317, 1013641, 1542132, 2346276, 3569413, 5430537, 8261962, 12569362

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..40.

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

Formula

a(n) = A159284(n+1) + A132380(n+7).

a(0)=0, a(1)=1, a(2)=1, a(3)=4, a(4)=4, a(5)=5, a(6)=9, a(n)= a(n-2)+ 2*a(n-3)-a(n-4)+a(n-6)+2*a(n-7). - Harvey P. Dale, Jul 19 2011

Mathematica

CoefficientList[Series[x(-1-x-3x^2-x^3+2x^5)/((2x^3+x^2-1)(x^4+1)), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 1, 2, -1, 0, 1, 2}, {0, 1, 1, 4, 4, 5, 9}, 51] (* Harvey P. Dale, Jul 19 2011 *)

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; 1; 4; 4; 5; 9])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016

Crossrefs

Cf. A107849, A107850, A107852.

Sequence in context: A096641 A155693 A160705 * A302337 A098821 A363322

Adjacent sequences: A107848 A107849 A107850 * A107852 A107853 A107854

Keyword

easy,nonn

Author

Creighton Dement, May 25 2005

Status

approved