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A085789 Partial sums of n 3-spaced triangular numbers beginning with t(2), e.g., a(2) = t(2) + t(5) = 3 + 15 = 18. 2
3, 18, 54, 120, 225, 378, 588, 864, 1215, 1650, 2178, 2808, 3549, 4410, 5400, 6528, 7803, 9234, 10830, 12600, 14553, 16698, 19044, 21600, 24375, 27378, 30618, 34104, 37845, 41850, 46128, 50688, 55539, 60690, 66150, 71928, 78033, 84474, 91260, 98400, 105903 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sums of rows of triangle A100345 (n>0).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 3/2 * n^2*(n+1).

a(n) = 3*n*binomial(n+1,2) = 3*n*A000217(n) = 3*A002411(n). - Arkadiusz Wesolowski, Feb 10 2012

G.f.: 3*(x + 2*x^2)/(1 - x)^4. - Arkadiusz Wesolowski, Feb 11 2012

MATHEMATICA

CoefficientList[Series[3 (1 + 2 x) / (1 - x)^4, {x, 0, 40}], x](* Vincenzo Librandi, Aug 14 2017 *)

PROG

(MAGMA) [3/2*n^2*(n+1): n in [1..40]]; // Vincenzo Librandi, Aug 14 2017

CROSSREFS

Cf. A004188.

Sequence in context: A267639 A238649 A268484 * A027334 A130505 A222204

Adjacent sequences:  A085786 A085787 A085788 * A085790 A085791 A085792

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jul 23 2003

EXTENSIONS

More terms from Reinhard Zumkeller, Nov 18 2004

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)