A193669 Expansion of o.g.f.(1-x^4)/(1-x+x^8).

1, 1, 1, 1, 0, 0, 0, 0, -1, -2, -3, -4, -4, -4, -4, -4, -3, -1, 2, 6, 10, 14, 18, 22, 25, 26, 24, 18, 8, -6, -24, -46, -71, -97, -121, -139, -147, -141, -117, -71, 0, 97, 218, 357, 504, 645, 762, 833, 833, 736, 518, 161, -343, -988, -1750, -2583, -3416, -4152

Offset: 0

Author

Johannes W. Meijer, Aug 11 2011

Keywords

• sign
• easy

Comments

The Gi1 sums, see A180662, of triangle A108299 equal the terms of this sequence.

Links

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

Crossrefs

Cf. A108299, A180662.

Programs

Maple

A193669 := proc(n) option remember: coeftayl((1-x^4) / (1-x+x^8) ,x=0,n) end: seq(A193669(n), n=0..57);

Mathematica

CoefficientList[Series[(1-x^4)/(1-x+x^8),{x,0,80}],x] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,-1},{1,1,1,1,0,0,0,0},80] (* Harvey P. Dale, Jul 16 2014 *)

Formula

G.f.: -(x-1)*(1+x)*(x^2+1) / ( (x^2-x+1)*(x^6+x^5-x^3-x^2+1) ).

a(n) = a(n-1) - a(n-8), a(0) = a(1) = a(2) = a(3) = 1, a(4) = a(5) = a(6) = a(7) = 0.