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A092441
Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.
3
1, 10, 65, 346, 1637, 7218, 30529, 126034, 513125, 2072698, 8335505, 33439914, 133972165, 536346850, 2146369793, 8587575586, 34354757957, 137428468074, 549733794193, 2198977118650, 8795996553701, 35184170762770
OFFSET
0,2
REFERENCES
J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 13).
LINKS
J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics
FORMULA
a(n) = 2^(2n+3)-2^(n+2)-2(n+2)(2^(n+1)-1)+(n+1)^2.
G.f.: -(8*x^4-2*x^2+x-1)/((x-1)^3*(2*x-1)^2*(4*x-1)). [Colin Barker, Nov 22 2012]
EXAMPLE
a(3) = 2^9-2^5-10(2^4-1)+4^2 = 346.
MATHEMATICA
LinearRecurrence[{11, -47, 101, -116, 68, -16}, {1, 10, 65, 346, 1637, 7218}, 30] (* Harvey P. Dale, Nov 26 2022 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004
STATUS
approved