A140675 a(n) = n*(3*n + 19)/2.

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

Offset: 0

Author

Omar E. Pol, May 22 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Sela Fried, Counting r X s rectangles in nondecreasing and Smirnov words, arXiv:2406.18923 [math.CO], 2024. See p. 5.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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.

Programs

Mathematica

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

PARI

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

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