A103780 Row sums of square of trinomial triangle A071675.

1, 1, 3, 9, 25, 69, 189, 519, 1428, 3930, 10812, 29742, 81816, 225070, 619156, 1703262, 4685565, 12889687, 35458707, 97544655, 268339161, 738183999, 2030697309, 5586319365, 15367609920, 42275319276, 116296719448

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,4,6,8,8,6,3,1).

Formula

G.f.: 1/(1-x-2*x^2-4*x^3-6*x^4-8*x^5-8*x^6-6*x^7-3*x^8-x^9).

a(n) = a(n-1) +2a(n-2) +4a(n-3) +6a(n-4) +8a(n-5) +8a(n-6) +6a(n-7) +3a(n-8) +a(n-9).

Mathematica

CoefficientList[Series[1/(1 - x - 2*x^2 - 4*x^3 - 6*x^4 - 8*x^5 - 8*x^6 - 6*x^7 - 3*x^8 - x^9), {x, 0, 50}], x] (* G. C. Greubel, Mar 03 2017 *)
LinearRecurrence[{1, 2, 4, 6, 8, 8, 6, 3, 1}, {1, 1, 3, 9, 25, 69, 189, 519, 1428}, 40] (* Harvey P. Dale, Jun 14 2020 *)

Prog

(Maxima)
a(n):=sum(sum((sum(binomial(j, n-3*k+2*j)*(-1)^(j-k)*binomial(k, j), j, 0, k)) *sum(binomial(j, -3*m+k+2*j)*binomial(m, j), j, 0, m), k, m, n), m, 0, n); /* Vladimir Kruchinin, Dec 01 2011 */
(PARI) x='x+O('x^50); Vec(1/(1 -x -2*x^2 -4*x^3 -6*x^4 -8*x^5 -8*x^6 -6*x^7 -3*x^8 -x^9)) \\ G. C. Greubel, Mar 03 2017

Crossrefs

Sequence in context: A000242 A077846 A005322 * A211288 A206727 A211296

Adjacent sequences: A103777 A103778 A103779 * A103781 A103782 A103783

Keyword

easy,nonn

Author

Paul Barry, Feb 15 2005

Status

approved