A134479 Row sums of triangle A134478.

1, 3, 9, 18, 30, 45, 63, 84, 108, 135, 165, 198, 234, 273, 315, 360, 408, 459, 513, 570, 630, 693, 759, 828, 900, 975, 1053, 1134, 1218, 1305, 1395, 1488, 1584, 1683, 1785, 1890, 1998, 2109, 2223, 2340, 2460, 2583, 2709, 2838, 2970, 3105, 3243, 3384, 3528, 3675, 3825

Offset: 0

Author

Gary W. Adamson, Oct 27 2007

Keywords

• nonn
• easy
• less

Comments

Essentially the same as A045943. - R. J. Mathar, Mar 28 2012

Examples

			a(3) = 18 = (1, 3, 3, 1) dot (1, 2, 4, -1) = (1 + 6 + 12 -1).
a(3) = 18 = sum of row 3 terms of triangle A134478: (3 = 4 + 5 + 6).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A045943, A134478.

Programs

Mathematica

Join[{1}, Table[Sum[n + k, {k, 0, n}], {n, 1, 50}]] (* G. C. Greubel, Sep 24 2017 *)

PARI

concat([1], for(n=1,50, print1(sum(k=0,n, n+k), ", "))) \\ G. C. Greubel, Sep 24 2017

PARI

Vec((1 + 3*x^2 - x^3) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Sep 25 2017

Formula

Binomial transform of [1, 2, 4, -1, 1, -1, 1, ...].

From Colin Barker, Sep 24 2017: (Start)

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

a(n) = 3*n*(1 + n) / 2 for n>0.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. (End)

Extensions

Terms a(14) onward added by G. C. Greubel, Sep 24 2017