A206450 Number of 0..3 arrays of length n avoiding the consecutive pattern 0..3.

4, 16, 64, 255, 1016, 4048, 16128, 64257, 256012, 1020000, 4063872, 16191231, 64508912, 257015648, 1023998720, 4079803649, 16254705684, 64761807088, 258023229632, 1028013114879, 4095797753832, 16318429208240, 65015693603328

Offset: 1

Author

R. H. Hardin, Feb 07 2012

Keywords

• nonn
• easy

Comments

Column 3 of A206455.

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (4,0,0,-1).

Crossrefs

Cf. A206455.

Formula

a(n) = 4*a(n-1) -a(n-4).

Empirical: a(n) = sum{i in 0..floor(n/4)} ((-1)^i*4^(n-4*i)*binomial(n-3*i,i)).

g.f.: x*(4 - x^3) / (1 - 4*x + x^4). - Colin Barker, Feb 23 2018