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A137200 Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type. 2
1, 1, 2, 2, 4, 5, 7, 9, 13, 18, 25, 34, 47, 65, 90, 124, 171, 236, 326, 450, 621, 857, 1183, 1633, 2254, 3111, 4294, 5927, 8181, 11292, 15586, 21513, 29694, 40986, 56572, 78085, 107779, 148765, 205337, 283422, 391201, 539966, 745303, 1028725, 1419926, 1959892 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Without the restriction one gets the Fibonacci numbers, A000045.

Might be called the no-tri-bonacci numbers.

LINKS

Table of n, a(n) for n=0..45.

Brian Rice, Proof of the recurrence

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

FORMULA

a(n) = a(n-1) + a(n-4) for n>4; g.f.: (1+x^2+x^4)/(1-x-x^4). Also a(n) = a(n-2) + a(n-4) + a(n-5).

EXAMPLE

For example (using 1's to denote squares and 2's to denote dominoes), a(6)=7 because you have the tilings 11211, 1122, 1212, 1221, 2112, 2121 and 2211 and no others.

MATHEMATICA

Join[{1}, LinearRecurrence[{1, 0, 0, 1}, {1, 2, 2, 4}, 50]] (* Harvey P. Dale, Jul 26 2011 *)

CROSSREFS

Cf. A000045.

Sequence in context: A240508 A174068 A135833 * A026930 A211862 A286948

Adjacent sequences:  A137197 A137198 A137199 * A137201 A137202 A137203

KEYWORD

nonn

AUTHOR

Barry Cipra, Mar 03 2008

STATUS

approved

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Last modified November 14 12:21 EST 2019. Contains 329114 sequences. (Running on oeis4.)