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 A181626 Number of closed walks of length n in a kite graph (K4 with one edge deleted). 1
 4, 0, 10, 12, 50, 100, 298, 700, 1890, 4692, 12250, 31020, 80018, 204100, 524170, 1340572, 3437250, 8799540, 22548538, 57746700, 147940850, 378927652, 970691050, 2486401660, 6369165858, 16314772500, 41791435930, 107050525932, 274216269650, 702418373380, 1799283451978 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is trace of A^n where A is adjacency matrix of the kite graph (K4 with one edge deleted). REFERENCES Godsil, Algebraic Combinatorics, Chapman & Hall, Inc, 1993, pages 22-23 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,5,4). FORMULA Generating function in terms of characteristic polynomial from Godsil (1993) is 2*x*(2 - 5*x^2 - 2*x^3) / ((1 + x)*(1 - x - 4*x^2)). From Colin Barker, Dec 25 2017: (Start) a(n) = 2^(-3-n) * ((-1)^(1+n)*2^(3+n) - (1-sqrt(17))^n*(1+sqrt(17)) + (-1+sqrt(17))*(1+sqrt(17))^n) for n>1. a(n) = 5*a(n-2) + 4*a(n-3) for n>4. (End) MATHEMATICA Series[2*x*(2 - 5*x^2 - 2*x^3) / ((1 + x)*(1 - x - 4*x^2)), {x, 0, 20}][[3]] PROG (PARI) Vec(2*x*(2 - 5*x^2 - 2*x^3) / ((1 + x)*(1 - x - 4*x^2)) + O(x^40)) \\ Colin Barker, Dec 25 2017 CROSSREFS Sequence in context: A293933 A158976 A211243 * A279432 A019127 A019207 Adjacent sequences:  A181623 A181624 A181625 * A181627 A181628 A181629 KEYWORD easy,nonn AUTHOR Yaroslav Bulatov (yaroslavvb(AT)gmail.com), Nov 02 2010 STATUS approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)