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A344679
Number of 2-matchings of the n-th centered square grid graph.
1
0, 0, 86, 544, 1854, 4688, 9910, 18576, 31934, 51424, 78678, 115520, 163966, 226224, 304694, 401968, 520830, 664256, 835414, 1037664, 1274558, 1549840, 1867446, 2231504, 2646334, 3116448, 3646550, 4241536, 4906494, 5646704, 6467638, 7374960, 8374526, 9472384, 10674774
OFFSET
1,3
COMMENTS
Number of ways two dominoes can be placed on an "other" Aztec Diamonds chessboard.
FORMULA
a(n) = 2*(n-2)*(4n^3-8n^2+n+4) for n > 1.
From Stefano Spezia, Aug 17 2021: (Start)
G.f.: 2*x^3*(43 + 57*x - 3*x^2 - x^3)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 6. (End)
EXAMPLE
For n=1 there is no way to place 2 dominoes in the centered square grid graphs, because they don't have enough space to be placed, so a(1)=0.
For n=2 there is no way to place 2 dominoes in the centered square grid graphs, because the first domino will cover the center square every time, so a(2)=0.
CROSSREFS
Sequence in context: A202524 A232708 A232706 * A231266 A202769 A232756
KEYWORD
nonn,easy
AUTHOR
Nicolas Bělohoubek, Aug 17 2021
STATUS
approved