OFFSET
0,4
COMMENTS
Except for p(0,x)=1 all sum to zero: Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 12}] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
LINKS
Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)
FORMULA
p(k, x) = x*p(k - 1, x) + p(k - 2, x) for k >= 3 with p(0,x) = 1, p(1,x) = x-1 and p(2,x) = x^2-3x+2. (Corrected by Robert Israel, Jul 12 2016)
G.f.: g(t,x) = (1 - t + (1-2x) t^2)/(1 - t x - t^2). - Robert Israel, Jul 12 2016
EXAMPLE
1
-1, 1
2, -3, 1
-1, 3, -3, 1
2, -4, 4, -3, 1
-1, 5, -7, 5, -3, 1
2, -5, 9, -10, 6, -3, 1
MAPLE
S:= series((1 - t + (1-2*x)*t^2)/(1 - t*x - t^2), t, 21):
R:= [seq(coeff(S, t, n), n=0..19)]:
seq(seq(coeff(R[n], x, j), j=0..n-1), n=1..20); # Robert Israel, Jul 12 2016
MATHEMATICA
p[0, x] = 1; p[1, x] = x - 1; p[2, x] = x^2 - 3x + 2; p[k_, x_] := p[k, x] = x*p[k - 1, x] + p[k - 2, x] ; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Oct 02 2006
EXTENSIONS
Edited by Robert Israel, Jul 13 2016
STATUS
approved