A134478 -id:A134478 - cp's OEIS frontend

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

Gary W. Adamson, Oct 27 2007

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

			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).

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

Cf. A045943, A134478.

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

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

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

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)

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

A134480 A134478 * A000012.

Original entry on oeis.org

1, 3, 2, 9, 7, 4, 18, 15, 11, 6, 30, 26, 21, 15, 8, 45, 40, 34, 27, 19, 10, 63, 57, 50, 42, 33, 23, 12, 84, 77, 69, 60, 50, 39, 27, 14, 108, 100, 91, 81, 70, 58, 45, 31, 16, 135, 126, 116, 105, 93, 80, 66, 51, 35, 18

Offset: 0

Gary W. Adamson, Oct 27 2007

Row sums = A134481: (1, 5, 20, 50, 100, 175, ...).

Left border = A134479.

			First few rows of the triangle:
   1;
   3,  2;
   9,  7,  4;
  18, 15, 11,  6;
  30, 26, 21, 15,  8;
  45, 40, 34, 27, 19, 10;
  63, 57, 50, 42, 33, 23, 12;
  ...

Cf. A134478, A134481, A134479.

A134478 * A000012 as infinite lower triangular matrices. Triangle read by rows, partial sums of A134478 terms starting from the right.

cp's OEIS Frontend

A134479 Row sums of triangle A134478.

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