

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
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OFFSET

1,1


COMMENTS

a(n) is the number of perfect matchings of an edgelabeled 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 length2 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+(1sqrt(2))^n+(1+sqrt(2))^n. G.f.: 2*x*(2x2*x^2x^3)/(1x)/(1+x)/(12*xx^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

SarahMarie Belcastro (smbelcas(AT)toroidalsnark.net), Jul 04 2009


STATUS

approved



