login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A140672
a(n) = n*(3*n + 13)/2.
16
0, 8, 19, 33, 50, 70, 93, 119, 148, 180, 215, 253, 294, 338, 385, 435, 488, 544, 603, 665, 730, 798, 869, 943, 1020, 1100, 1183, 1269, 1358, 1450, 1545, 1643, 1744, 1848, 1955, 2065, 2178, 2294, 2413, 2535, 2660, 2788, 2919, 3053
OFFSET
0,2
LINKS
FORMULA
a(n) = (3*n^2 + 13*n)/2.
a(n) = 3*n + a(n-1) + 5 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=8, a(2)=19; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 16 2011
G.f.: x*(8 - 5*x)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 24 2011
E.g.f.: (1/2)*(3*x^2 +16*x)*exp(x). - G. C. Greubel, Jul 17 2017
MATHEMATICA
Table[n (3 n + 13)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 8, 19}, 50] (* Harvey P. Dale, Dec 16 2011 *)
PROG
(PARI) a(n)=n*(3*n+13)/2 \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [(3*n^2 + 13*n)/2 : n in [0..80]]; // Wesley Ivan Hurt, Dec 27 2023
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: A017485 A146270 A146222 * A230098 A262713 A135027
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, May 22 2008
STATUS
approved