A044043 Number of tilings of 2 X n rectangle with polyominoes, each of which has area = # of adjacent polyominoes.

0, 0, 2, 5, 3, 9, 23, 25, 44, 113, 161, 244, 561, 930, 1405, 2865, 5137, 8062, 15082, 27806, 45582, 81210, 149637, 254034, 442904, 806389, 1400830, 2428499, 4362924, 7674434, 13329558, 23699803, 41904969, 73097351, 129121535, 228531847

Offset

1,3

Links

Table of n, a(n) for n=1..36.

Formula

Complicated linear recurrence in terms of 4 variables known.

Empirical g.f.: -x^3*(2*x^8 + 4*x^5 + 4*x^4 + 3*x^3 + 3*x^2 + 5*x + 2) / (2*x^10 + 4*x^7 + 3*x^6 + x^5 + 2*x^4 + 3*x^3 - 1). [Colin Barker, Nov 29 2012]

Example

a(5)=3 because of the tilings
  aaabb aabbb abbbc
  ccddd cccdd adddc

Crossrefs

Sequence in context: A361398 A332357 A305126 * A133128 A057337 A163233

Adjacent sequences: A044040 A044041 A044042 * A044044 A044045 A044046

Keyword

nonn

Author

I seem to have no record of the source for this sequence. - N. J. A. Sloane

Status

approved