A344679 Number of 2-matchings of the n-th centered square grid graph.

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

Author

Nicolas Bělohoubek, Aug 17 2021

Keywords

• nonn
• easy

Comments

Number of ways two dominoes can be placed on an "other" Aztec Diamonds chessboard.

Examples

			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.
		

Links

• Nicolas Bělohoubek, Visualization of 3rd term.
• Ron Knott, 1.2.5 The "other" Aztec Diamonds
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A001844, A242856.

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)