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 A140766 a(n) = 6*a(n-1) - 6*a(n-2). 2
 1, 5, 24, 114, 540, 2556, 12096, 57240, 270864, 1281744, 6065280, 28701216, 135815616, 642686400, 3041224704, 14391229824, 68100030720, 322252805376, 1524916647936, 7215983055360, 34146398444544, 161582492335104, 764616563343360, 3618204426049536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Companion sequence = A030192 beginning (1, 6, 30, 144, 684,...). LINKS Index entries for linear recurrences with constant coefficients, signature (6, -6). FORMULA a(n) = 6*a(n-1) - 6*a(n-2); a(1) = 1, a(2) = 5. Term (1,1) of M^n, where M = the 3x3 matrix [1,1,1; 1,2,1; 3,1,3]. O.g.f.: x(1-x)/(1-6x+6x^2). a(n)=A030192(n-1)-A030192(n-2). - R. J. Mathar, May 31 2008 a(n)=(1/2)*[3-sqrt(3)]^n+(1/3)*sqrt(3)*[3+sqrt(3)]^n+(1/2)*[3+sqrt(3)]^n-(1/3)*[3-sqrt(3)]^n *sqrt(3), with n>=0 - Paolo P. Lava, Jun 25 2008 a(n) = Sum_{1<=k<=n} A030523(n,k)*2^(k-1). - Philippe Deléham, Feb 19 2013 EXAMPLE a(5) = 540 = 6*a(4) - 6*a(3) = 6*(114) - 6*24. a(5) = 540 = term (1,1) of X^5. MATHEMATICA LinearRecurrence[{6, -6}, {1, 5}, 30] (* Harvey P. Dale, Oct 01 2014 *) CROSSREFS Cf. A030192, A030523. Sequence in context: A347029 A141223 A289783 * A026388 A242509 A057969 Adjacent sequences:  A140763 A140764 A140765 * A140767 A140768 A140769 KEYWORD nonn,easy AUTHOR Gary W. Adamson and Roger L. Bagula, May 28 2008 EXTENSIONS More terms from R. J. Mathar, May 31 2008 More terms from Harvey P. Dale, Oct 01 2014 STATUS approved

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Last modified December 9 08:17 EST 2021. Contains 349627 sequences. (Running on oeis4.)