OFFSET
1,1
COMMENTS
Column 4 of A209650.
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
Robert Israel, Maple-assisted proof of formula
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
Empirical: a(n) = 9*n^3 + (9/2)*n^2 - (9/2)*n.
Formula confirmed by Robert Israel, Mar 07 2018: see link.
From Colin Barker, Jul 12 2018: (Start)
G.f.: 9*x*(1 + 5*x) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
EXAMPLE
Some solutions for n=4:
0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1
0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0
0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0
MAPLE
seq(9*n^3 + (9/2)*n^2 - (9/2)*n, n=1..100); # Robert Israel, Mar 07 2018
PROG
(PARI) Vec(9*x*(1 + 5*x) / (1 - x)^4 + O(x^40)) \\ Colin Barker, Jul 12 2018
(PARI) a(n) = 9*n^3+(9/2)*n^2-(9/2)*n; \\ Altug Alkan, Jul 12 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Mar 11 2012
STATUS
approved