OFFSET

0,4

LINKS

Paul Tek, Table of n, a(n) for n = 0..1000

Paul Tek, Illustration of the formula

Paul Tek, Illustration of the first terms

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,1).

FORMULA

[0 1 0 0 1 0 0] [1]

[0 0 1 0 0 0 0] [0]

[0 0 0 1 0 0 0] [0]

a(n) = [1 0 0 0 0 0 0] * [0 0 0 0 1 0 1]^n * [1], for any n>=0.

[0 0 0 0 0 1 0] [0]

[0 0 0 0 0 0 1] [0]

[0 1 1 0 0 0 0] [1]

G.f.: (x^6+x^3+1)/(-x^6-x^5-x^4-x^3+1) = -(x^6+x^3+1)/((x^2+x+1)*(x^4+x-1)). - Colin Barker, Jul 27 2014

a(n) = a(n-3)+a(n-4)+a(n-5)+a(n-6) for n>6. - Colin Barker, Jul 28 2014

EXAMPLE

A 3 X 1 rectangle can be tiled in three ways:

+-+-+-+ +-+---+ +---+-+

| | | |, | | | and | | |.

+-+-+-+ +-+---+ +---+-+

The first tiling is not acceptable, as none of the 1 X 1 tiles is next to a 2 X 1 tile.

The second and third tilings are acceptable, as every 1 X 1 tile is next to a 2 X 1 tile and vice versa.

Hence, a(3)=2.

PROG

(PARI) Vec(-(x^6+x^3+1)/((x^2+x+1)*(x^4+x-1)) + O(x^100)) \\ Colin Barker, Jul 28 2014

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Paul Tek, Jul 27 2014

STATUS

approved