A099604 Antidiagonal sums of triangle A099602, in which row n equals the inverse binomial transform of column n of the triangle of trinomial coefficients (A027907).

1, 1, 2, 4, 7, 12, 23, 40, 72, 131, 233, 420, 756, 1355, 2438, 4381, 7868, 14144, 25413, 45661, 82058, 147444, 264943, 476092, 855483, 1537236, 2762296, 4963591, 8919173, 16027012, 28799164, 51749715, 92989886, 167094985, 300255720

Offset: 0

Author

Paul D. Hanna, Oct 25 2004

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 2, 3, 0, -2, -1).

Crossrefs

Cf. A099602, A027907.

Programs

Mathematica

LinearRecurrence[{0, 2, 3, 0, -2, -1}, {1, 1, 2, 4, 7, 12}, 35] (* Jean-François Alcover, Oct 30 2017 *)

PARI

a(n)=polcoeff((1+x-x^3)/(1-2*x^2-3*x^3+2*x^5+x^6)+x*O(x^n),n,x)

Formula

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

a(n) = 2*a(n-2) + 3*a(n-3) - 2*a(n-5) - a(n-6) for n>=6.