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

1,1

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).

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

Crossrefs

Cf. A206455.

Sequence in context: A269651 A077821 A215877 * A294452 A270142 A000302

Adjacent sequences: A206447 A206448 A206449 * A206451 A206452 A206453

Keyword

nonn,easy

Author

R. H. Hardin, Feb 07 2012

Status

approved