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 A164549 a(n) = 4*a(n-1)+2*a(n-2) for n > 1; a(0) = 1, a(1) = 6. 8
 1, 6, 26, 116, 516, 2296, 10216, 45456, 202256, 899936, 4004256, 17816896, 79276096, 352738176, 1569504896, 6983495936, 31072993536, 138258966016, 615181851136, 2737245336576, 12179345048576, 54191870867456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A123011. Inverse binomial transform of A164550. INVERT transform of the sequence (1, 5, 5*3, 5*3^2, 5*3^3, 5*3^4...); i.e. of (1, 5, 15, 45, 135, 405,...). The sequence can also be obtained by extracting the upper left terms in matrix powers of [(1,5); (1,3)]. - Gary W. Adamson, Jul 31 2016 The sequence is A090017 (1, 4, 18, 80, 356,...) convolved with (1, 2, 0, 0, 0,...). Also, the upper left terms extracted from matrix powers of [(1,5); (1,3)]. - Gary W. Adamson, Aug 20 2016 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4, 2). FORMULA a(n) = ((3+2*sqrt(6))*(2+sqrt(6))^n+(3-2*sqrt(6))*(2-sqrt(6))^n)/6. G.f.: (1+2*x)/(1-4*x-2*x^2). MATHEMATICA LinearRecurrence[{4, 2}, {1, 6}, 30] (* Harvey P. Dale, Mar 16 2013 *) CoefficientList[Series[(1 + 2 x)/(1 - 4 x - 2 x^2), {x, 0, 24}], x] (* Michael De Vlieger, Aug 02 2016 *) PROG (MAGMA) [ n le 2 select 5*n-4 else 4*Self(n-1)+2*Self(n-2): n in [1..22] ]; (PARI) Vec((1+2*x)/(1-4*x-2*x^2) + O(x^30)) \\ Michel Marcus, Feb 04 2016 CROSSREFS Cf. A123011, A164550. Cf. A084057, A108306. Sequence in context: A289789 A124465 A287806 * A283341 A046647 A233075 Adjacent sequences:  A164546 A164547 A164548 * A164550 A164551 A164552 KEYWORD nonn AUTHOR Klaus Brockhaus, Aug 15 2009 STATUS approved

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Last modified January 16 15:53 EST 2019. Contains 319195 sequences. (Running on oeis4.)