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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). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..34.

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.

MATHEMATICA

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

PROG

(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)

CROSSREFS

Cf. A099602, A027907.

Sequence in context: A082548 A270995 A007323 * A026790 A054165 A054171

Adjacent sequences:  A099601 A099602 A099603 * A099605 A099606 A099607

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 25 2004

STATUS

approved

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Last modified December 16 01:36 EST 2017. Contains 296063 sequences.