A111663 Expansion of (-1+x^3+x^6+x^9)/((1-x)*(2*x-1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1)).

1, 2, 4, 8, 16, 32, 62, 124, 248, 494, 988, 1976, 3952, 7904, 15808, 31616, 63232, 126464, 252926, 505852, 1011704, 2023406, 4046812, 8093624, 16187248, 32374496, 64748992, 129497984, 258995968, 517991936, 1035983870, 2071967740

Offset: 0

Author

Creighton Dement, Aug 14 2005

Keywords

• nonn
• easy

Comments

Initial terms factored: [1,2,(2)^2,(2)^3,(2)^4,(2)^5,(2) (31),(2)^2 (31),(2)^3 (31),(2) (13) (19),(2)^2 (13) (19),(2)^3 (13) (19),(2)^4 (13) (19),(2)^5 (13) (19),(2)^6 (13) (19),(2)^7 (13) (19),(2)^8 (13) (19),(2)^9 (13) (19),(2) (17) (43) (173),(2)^2 (17) (43) (173),(2)^3 (17) (43) (173),(2) (7)^2 (11) (1877),(2)^2 (7)^2 (11) (1877),(2)^3 (7)^2 (11) (1877),(2)^4 (7)^2 (11) (1877),(2)^5 (7)^2 (11) (1877),(2)^6 (7)^2 (11) (1877),(2)^7 (7)^2 (11) (1877),(2)^8 (7)^2 (11) (1877),(2)^9 (7)^2 (11) (1877)]

Floretion Algebra Multiplication Program, FAMP Code: 2jbaseksumseq[.5'i + .5i' + .5'ii' + .5'jj' + .5'kk' + .5e], sumtype: sum[(Y[0], Y[1], Y[2]),mod(3)

Links

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

Crossrefs

Cf. A111662.

Programs

Mathematica

CoefficientList[Series[(-1+x^3+x^6+x^9)/((1-x)(2x-1)(x^2+1)*(x^2+x+1)(x^4-x^2+1)),{x,0,40}],x] (* or *) LinearRecurrence[{2,0,1,-2,0,-1,2,0,1,-2},{1,2,4,8,16,32,62,124,248,494},40] (* Harvey P. Dale, May 04 2012 *)

PARI

Vec((-1+x^3+x^6+x^9)/((1-x)*(2*x-1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=16, a(5)=32, a(6)=62, a(7)=124, a(8)=248, a(9)=494, a(n) = 2*a(n-1)+a(n-3)-2*a(n-4)-a(n-6)+2*a(n-7)+ a(n-9)- 2*a(n-10). [Harvey P. Dale, May 04 2012]