OFFSET
0,1
COMMENTS
The even rows which start with 4, 8, 16 ... appear to be the absolute values of the Riordan array A128414. - Georg Fischer, Feb 25 2020
LINKS
Eric Weisstein's World of Mathematics, Jacobsthal-Lucas Polynomial.
FORMULA
Let p(n, x) = 2*x*p(n-2, x) + p(n-1, x) with p(0, x) = 2 and p(1, x) = 1. The coefficients of the polynomial p(n, x), listed in reverse order, give row n. - Jinyuan Wang, Feb 25 2020
EXAMPLE
The triangle starts:
2;
1;
4, 1;
6, 1;
8, 8, 1;
20, 10, 1;
16, 36, 12, 1;
56, 56, 14, 1;
32, 128, 80, 16, 1;
144, 240, 108, 18, 1;
64, 400, 400, 140, 20, 1;
352, 880, 616, 176, 22, 1;
...
MAPLE
b:= proc(n) option remember;
`if`(n<2, 2-n, b(n-1)+2*expand(x*b(n-2)))
end:
T:= n-> (p-> (d-> seq(coeff(p, x, d-i), i=0..d))(degree(p)))(b(n)):
seq(T(n), n=0..20); # Alois P. Heinz, Feb 25 2020
MATHEMATICA
f[0] = 2; f[1] = 1; f[n_] := 2 x f[n - 2] + f[n - 1];
Table[Reverse[CoefficientList[f[n], x]], {n, 0, 14}] // Flatten (* Jinyuan Wang, Feb 25 2020 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Apr 09 2008
EXTENSIONS
Offset set to 0 by Peter Luschny, Feb 25 2020
STATUS
approved