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A162485
a(1)=4, a(2)=6; for n > 2, a(n) = 2*a(n-1) + a(n-2) - 4*((n-1) mod 2).
0
4, 6, 16, 34, 84, 198, 480, 1154, 2788, 6726, 16240, 39202, 94644, 228486, 551616, 1331714, 3215044, 7761798, 18738640, 45239074, 109216788, 263672646, 636562080, 1536796802, 3710155684
OFFSET
1,1
COMMENTS
a(n) is the number of perfect matchings of an edge-labeled 2 X n Klein bottle grid graph, or equivalently the number of domino tilings of a 2 X n Klein bottle grid. (The twist is on the length-2 side.)
FORMULA
For n > 1, a(n) = (1/2)*((1 + sqrt(2))^n*(2 + (-1 + sqrt(2))^(2*floor((1/2)*(-1 + n)))*(-4 + 3*sqrt(2))) + (1 - sqrt(2))^n*(2 - (-1 - sqrt(2))^(2*floor((1/2)*(-1 + n)))*(4 + 3*sqrt(2)))).
From Colin Barker, May 01 2012: (Start)
a(n) = 1 - (-1)^n + (1-sqrt(2))^n + (1+sqrt(2))^n.
G.f.: 2*x*(2-x-2*x^2-x^3)/(1-x)/(1+x)/(1-2*x-x^2). (End)
a(n) = A002203(n) + 1 - (-1)^n. - R. J. Mathar, Oct 08 2016
EXAMPLE
a(3) = 2*a(2) + a(1) - 4*(2 mod 2) = 2*6 + 4 - 0 = 16.
CROSSREFS
Sequence in context: A183370 A113883 A036748 * A188466 A076066 A227178
KEYWORD
easy,nonn
AUTHOR
STATUS
approved