OFFSET
0,2
COMMENTS
a(n) equals the number of vertices of the A256666(n)-th graph (see Illustration of initial terms in A256666 Links). - Ivan N. Ianakiev, Apr 20 2015
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) = A055998(n)*3 = (3*n^2 + 15*n)/2 = n*(3*n + 15)/2.
a(n) = 3*n + a(n-1) + 6 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
G.f.: 3*x*(3 - 2*x)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 24 2011
E.g.f.: (1/2)*(3*x^2 + 18*x)*exp(x). - G. C. Greubel, Jul 17 2017
From Amiram Eldar, Feb 25 2022: (Start)
Sum_{n>=1} 1/a(n) = 137/450.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/15 - 47/450. (End)
MATHEMATICA
Table[Sum[i + n - 3, {i, 6, n}], {n, 5, 52}] (* Zerinvary Lajos, Jul 11 2009 *)
Table[3 n (n + 5)/2, {n, 0, 50}] (* Bruno Berselli, Sep 05 2018 *)
LinearRecurrence[{3, -3, 1}, {0, 9, 21}, 50] (* Harvey P. Dale, Jul 20 2023 *)
PROG
(PARI) concat(0, Vec(3*x*(3 - 2*x)/(1 - x)^3 + O(x^100))) \\ Michel Marcus, Apr 20 2015
(PARI) a(n) = 3*n*(n+5)/2; \\ Altug Alkan, Sep 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, May 22 2008
STATUS
approved