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A134479 Row sums of triangle A134478. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 17:07 EDT 2022. Contains 353847 sequences. (Running on oeis4.)