A118403 Unsigned row sums of triangle A118401; a(n) = A118402(n^2-n+2), where A118402 is the row sums of triangle A118400.

1, 1, 3, 5, 9, 15, 23, 33, 45, 59, 75, 93, 113, 135, 159, 185, 213, 243, 275, 309, 345, 383, 423, 465, 509, 555, 603, 653, 705, 759, 815, 873, 933, 995, 1059, 1125, 1193, 1263, 1335, 1409, 1485, 1563, 1643, 1725, 1809, 1895, 1983, 2073, 2165, 2259, 2355

Offset: 0

Author

Paul D. Hanna, Apr 27 2006

Keywords

• nonn
• easy

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A027688, A118400, A118401, A118402.

Programs

Maple

seq(coeff(series((1-2*x+2*x^2)*(1+x^2)/(1-x)^3,x,n+1), x, n), n = 0 .. 55); # Muniru A Asiru, Jan 02 2019

Mathematica

Join[{1, 1}, Table[n^2 + n + 3, {n, 0, 47}]] (* Jon Maiga, Jan 02 2019 *)

PARI

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

Formula

G.f.: A(x) = (1-2*x+2*x^2)*(1+x^2)/(1-x)^3.

a(n) = A027688(n-2) for n > 1. - Jon Maiga, Jan 02 2019

E.g.f.: exp(x)*(5 - 2*x + x^2) - 2*(2 + x). - Stefano Spezia, Dec 21 2024