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A140675 a(n) = n*(3*n + 19)/2. 14
0, 11, 25, 42, 62, 85, 111, 140, 172, 207, 245, 286, 330, 377, 427, 480, 536, 595, 657, 722, 790, 861, 935, 1012, 1092, 1175, 1261, 1350, 1442, 1537, 1635, 1736, 1840, 1947, 2057, 2170, 2286, 2405, 2527, 2652, 2780, 2911, 3045, 3182 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = (3*n^2 + 19*n)/2.

a(n) = 3*n + a(n-1) + 8 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

G.f.: x*(11 - 8*x)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 24 2011

E.g.f.: (1/2)*(3*x^2 + 22*x)*exp(x). - G. C. Greubel, Jul 17 2017

MATHEMATICA

Table[(n(3n+19))/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 11, 25}, 50] (* Harvey P. Dale, Apr 26 2018 *)

PROG

(PARI) a(n)=n*(3*n+19)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.

Sequence in context: A240895 A301635 A031025 * A161532 A118648 A262105

Adjacent sequences:  A140672 A140673 A140674 * A140676 A140677 A140678

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, May 22 2008

STATUS

approved

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Last modified September 20 00:54 EDT 2018. Contains 315220 sequences. (Running on oeis4.)