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

Author

Paul Barry, Feb 15 2005

Keywords

• easy
• nonn

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).

Programs

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 *)

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

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).