A107854 G.f. x*(x^2+1)*(x^3-x-1)/((2*x^3+x^2-1)*(x^4+1)).

0, 1, 1, 2, 3, 3, 5, 8, 11, 19, 29, 42, 67, 99, 149, 232, 347, 531, 813, 1226, 1875, 2851, 4325, 6600, 10027, 15251, 23229, 35306, 53731, 81763, 124341, 189224, 287867, 437907, 666317, 1013642, 1542131, 2346275, 3569413, 5430536, 8261963, 12569363

Offset: 0

Author

Creighton Dement, May 25 2005

Keywords

• easy
• nonn

Comments

The sequence A078028 is given by 1em[I* ]forzapseq and is from the same "batch" (i.e., corresponding to the same floretion and symmetry settings) as A107849, A107850, A107851, A107852, A107853 and (a(n)).

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

Links

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

Crossrefs

Cf. A107849, A107850, A107851, A107852, A107853, A078028.

Programs

Mathematica

CoefficientList[Series[x(x^2+1)(x^3-x-1)/((2x^3+x^2-1)(x^4+1)),{x,0,50}],x] (* or *) LinearRecurrence[{0,1,2,-1,0,1,2},{0,1,1,2,3,3,5},50] (* Harvey P. Dale, Jun 21 2022 *)

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;2;3;3;5])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

Formula

a(n) = A159284(n) + A014017(n+5).