OFFSET
0,2
COMMENTS
For n >= 3, number of vertices of 4,4'-bipyridinium dendrimers (see the Arjomanfar and Gholami reference, p. 71). - Emeric Deutsch, Apr 12 2015
Number of ways to color a (2n-1) X (2n-1) chess board in a "balanced" way. A coloring is called balanced if, within every square subgrid made up of k^2 cells for 1 <= k <= 2*n-1, the number of black cells differs from the number of white cells by at most one. It is problem 3 from the British Maths Olympiad 2020. - Ruediger Jehn, Jan 27 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
A. Arjomanfar and N. Gholami, Computing the Szeged index of 4,4'-bipyridinium dendrimer, Iranian J. Math. Chem., 3, 2012, 67-72.
British Mathematical Olympiad, 2020 - Round 2, Problem 3.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
Row sums of triangle A131131.
a(n) = 4*2^n - 6 for n >= 1; a(0)=1.
From Philippe Deléham, Jan 04 2009: (Start)
a(n) = 3*a(n-1) - 2*a(n-2), n > 2; a(0)=1, a(1)=2, a(2)=10.
G.f.: (1-x+6*x^2) / (1-3*x+2*x^2). (End)
a(n) = 2*a(n-1) + 6 for n > 1, a(0)=1, a(1)=2. - Philippe Deléham, Sep 25 2009
E.g.f.: 3 - 6*exp(x) + 4*exp(2*x). - Stefano Spezia, Feb 05 2021
MAPLE
1, seq(4*2^n -6, n = 1..30);
MATHEMATICA
Join[{1}, LinearRecurrence[{3, -2}, {2, 10}, 30]] (* Harvey P. Dale, Mar 07 2014 *)
CoefficientList[Series[(1 -x +6x^2)/(1 -3x +2x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 08 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 16 2007
EXTENSIONS
Edited by Emeric Deutsch, Jul 12 2007
STATUS
approved