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 A092165 Let M = 2 X 2 matrix [ 1 2 / 5 4 ]; a(n) = (1,2) entry of M^n. 3
 2, 10, 62, 370, 2222, 13330, 79982, 479890, 2879342, 17276050, 103656302, 621937810, 3731626862, 22389761170, 134338567022, 806031402130, 4836188412782, 29017130476690, 174102782860142, 1044616697160850, 6267700182965102, 37606201097790610, 225637206586743662 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..23. Index entries for linear recurrences with constant coefficients, signature (5,6). FORMULA a(n) = (2*6^n - 2*(-1)^n)/7. a(n) = A092164(n) -(-1)^n. From R. J. Mathar, Apr 20 2009: (Start) a(n) = 5*a(n-1) + 6*a(n-2) = 2*A015540(n). G.f.: 2*x/((1+x)*(1-6*x)). (End) MATHEMATICA Table[ MatrixPower[{{1, 2}, {5, 4}}, n][[1, 2]], {n, 20}] (* Robert G. Wilson v, Apr 22 2004 *) LinearRecurrence[{5, 6}, {2, 10}, 25] (* Vincenzo Librandi, Jul 21 2015 *) PROG (Magma) [(2*6^n - 2*(-1)^n)/7: n in [1..30]]; // Vincenzo Librandi, Jul 21 2015 CROSSREFS Cf. A092164, A092166, A092167. Sequence in context: A356343 A352277 A155626 * A370249 A370275 A304443 Adjacent sequences: A092162 A092163 A092164 * A092166 A092167 A092168 KEYWORD nonn AUTHOR Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Apr 01 2004 EXTENSIONS Edited by Robert G. Wilson v, Apr 22 2004 More terms from Vincenzo Librandi, Jul 21 2015 STATUS approved

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Last modified April 12 16:59 EDT 2024. Contains 371635 sequences. (Running on oeis4.)