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 A331211 Number of green nodes in n-th power graph W exponentiation of a cycle graph with 7 blue nodes and one green node. 2
 1, 15, 117, 891, 6777, 51543, 392013, 2981475, 22675761, 172461663, 1311666021, 9975943179, 75872547369, 577052549415, 4388802753213, 33379264377459, 253867706760033, 1930803860947887, 14684827767302997, 111686210555580315, 849435201142733529, 6460422977475127287 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Thezebraherd user, Graph W multiplication, Youtube video. Index entries for linear recurrences with constant coefficients, signature (8,-3). FORMULA a(n) = a(n-1) + 2*b(n-1), b(n) = 2*a(n-1) + 7*b(n-1) with a(0) = 1 and b(0) = 7 where b(n) = A332936(n). From Colin Barker, Mar 03 2020: (Start) G.f.: (1 + 7*x) / (1 - 8*x + 3*x^2). a(n) = 8*a(n-1) - 3*a(n-2) for n>1. (End) From Stefano Spezia, Mar 03 2020: (Start) a(n) = ((4 - sqrt(13))^n*(-11 + sqrt(13)) + (4 + sqrt(13))^n*(11 + sqrt(13)))/(2*sqrt(13)). E.g.f.: exp(4*x)*cosh(sqrt(13)*x) + (11*exp(4*x)*sinh(sqrt(13)*x))/sqrt(13). (End) EXAMPLE For n = 2 take g(1)=15 and b(1)=51. Multiply b(1) by 2 to get 102 add 15 to get 117. For n = 3 take g(2)=117 and b(2)=387. Multiply b(2) by 2 to get 774 add 177 to get 891. PROG (Python) g=1 b=7 sg=0 sb=0 bl=[] gl=[] for int in range(1, 20):   sg=g*1+b*2   sb=b*7+g*2   g=sg   b=sb   gl.append(g)   bl.append(b) print(gl) (PARI) Vec((1 + 7*x) / (1 - 8*x + 3*x^2) + O(x^20)) \\ Colin Barker, Mar 03 2020 CROSSREFS Cf. A332936 (number of blue nodes). Similar sequences with a cycle size 3..6 are: A007483, A048876, A189274(n+1), A054490. Sequence in context: A125352 A126510 A328725 * A183475 A253804 A161476 Adjacent sequences:  A331208 A331209 A331210 * A331212 A331213 A331214 KEYWORD nonn,easy AUTHOR George Strand Vajagich, Mar 01 2020 EXTENSIONS a(14)-a(21) from Stefano Spezia, Mar 03 2020 Typo in a(14) fixed by Colin Barker, Apr 26 2020 STATUS approved

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Last modified November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)