A104187 Expansion of g.f. -(1+x^2+x^4)/((x^3+x^2+x-1)*(x-1)^2).

1, 3, 8, 18, 38, 76, 147, 279, 523, 973, 1802, 3328, 6136, 11302, 20805, 38285, 70437, 129575, 238348, 438414, 806394, 1483216, 2728087, 5017763, 9229135, 16975057, 31222030

Offset: 0

Author

Creighton Dement, Apr 01 2005

Keywords

• nonn

Comments

A floretion-generated sequence involving tribonacci numbers.

Floretion Algebra Multiplication Program, FAMP Code: 1tesforrokseq[A*B] = A = - .5'ii' + .5'jj' + .5'kk' + .5e B = + 'kj', 1vesforrokseq[A*B] = A000004, ForType: 1A.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,-1,1).

Crossrefs

Cf. A081172.

Programs

Mathematica

CoefficientList[Series[-(1+x^2+x^4)/((x^3+x^2+x-1)*(x-1)^2), {x,0,30}], x] (* or *) LinearRecurrence[{3,-2,0,-1,1},{1,3,8,18,38},30] (* Harvey P. Dale, Jun 14 2011 *)

Formula

a(n+2) - 2*a(n+1) + a(n) = A081172(n+4).

a(n) = (1/2) [A000073(n+3) + A000073(n+6) - 3n - 6 ]. - Ralf Stephan, May 20 2007

a(0)=1, a(1)=3, a(2)=8, a(3)=18, a(4)=38, a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5). - Harvey P. Dale, Jun 14 2011

Extensions

Definition corrected by Harvey P. Dale, Jun 14 2011