|
|
A193669
|
|
Expansion of o.g.f.(1-x^4)/(1-x+x^8).
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,10
|
|
COMMENTS
|
The Gi1 sums, see A180662, of triangle A108299 equal the terms of this sequence.
|
|
LINKS
|
|
|
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.
|
|
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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|