OFFSET
0,2
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).
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
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, May 22 2008
STATUS
approved