OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Kaie Kubjas, Luca Sodomaco, and Elias Tsigaridas, Exact solutions in low-rank approximation with zeros, arXiv:2010.15636 [math.AG], 2020.
Yuriy Sibirmovsky, Six verticals of the triangular spiral.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = C(n, 0) + 24*C(n, 1) + 36*C(n, 2).
a(n) = 18*n^2 + 6*n + 1.
G.f.: (1 + 22*x + 13*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(1 + 24*x + 18*x^2). - Stefano Spezia, Mar 07 2023
MATHEMATICA
Table[n^2 + (n + 1)^2, {n, 0, 300, 3}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 25, 85}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
Table[n^2 + (n + 1)^2, {n, 0, 150, 3}] (* Vincenzo Librandi, Aug 07 2013 *)
PROG
(PARI) x='x+O('x^99); Vec((1+22*x+13*x^2)/(1-x)^3) \\ Altug Alkan, Sep 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 15 2003
STATUS
approved