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

0,2

Comments

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

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).

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)

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A045943, A134478.

Sequence in context: A100967 A193567 A045943 * A184969 A194113 A330010

Adjacent sequences: A134476 A134477 A134478 * A134480 A134481 A134482

Keyword

nonn,easy,less

Author

Gary W. Adamson, Oct 27 2007

Extensions

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

Status

approved