OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
N. J. Calkin and H. S. Wilf, The number of independent sets in a grid graph, preprint.
N. J. Calkin and H. S. Wilf, The number of independent sets in a grid graph, SIAM J. Discrete Math, 11 (1998) 54-60.
Reinhardt Euler, The Fibonacci Number of a Grid Graph and a New Class of Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.6.
Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799 (set omega = 1 in Eq. (48)).
Index entries for linear recurrences with constant coefficients, signature (4,9,-5,-4,1).
FORMULA
From Yong Kong (ykong(AT)curagen.com), Dec 24 2000: (Start)
a(n) = 4*a(n - 1) + 9*a(n - 2) - 5*a(n - 3) - 4*a(n - 4) + a(n - 5);
G.f.: (1 + 4*x - 4*x^3 + x^4)/(1 - 4*x - 9*x^2 + 5*x^3 + 4*x^4 - x^5). (End)
a(n) = 2*a(n - 1) + 18*a(n - 2) + 9*a(n - 3) - 23*a(n - 4) - 2*a(n - 5) + 6*a(n - 6) - a(n - 7).
MATHEMATICA
LinearRecurrence[{4, 9, -5, -4, 1}, {1, 8, 41, 227, 1234}, 24] (* Jean-François Alcover, Nov 05 2017 *)
PROG
(PARI) Vec((1+4*x-4*x^3+x^4)/(1-4*x-9*x^2+5*x^3+4*x^4-x^5) + O(x^50)) \\ Michel Marcus, Sep 17 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Stephen G Penrice, Dec 06 1999
EXTENSIONS
More terms from James A. Sellers, Dec 08 1999
More terms from Michel Marcus, Sep 17 2014
STATUS
approved