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A162485 a(1) = 4, a(2) = 6; a(n) = 2 a(n - 1) + a(n - 2) - 4 Mod[n - 1, 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 (list; graph; refs; listen; history; text; internal format)
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.)

REFERENCES

S.-M. Belcastro, Tilings of 2 x n Grids on Surfaces, preprint.

LINKS

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1).

FORMULA

for n > 1, 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]))).

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). [Colin Barker, May 01 2012]

a(n) = A002203(n)+1-(-1)^n. - R. J. Mathar, Oct 08 2016

EXAMPLE

a(3) = 2 a(2) + a(1) - 4 Mod[2,2] = 2*6 + 4 - 0 = 16

CROSSREFS

Sequence in context: A183370 A113883 A036748 * A188466 A076066 A227178

Adjacent sequences:  A162482 A162483 A162484 * A162486 A162487 A162488

KEYWORD

easy,nonn

AUTHOR

Sarah-Marie Belcastro (smbelcas(AT)toroidalsnark.net), Jul 04 2009

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)