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 A011918 a(n) = A011916(n) + A011922(n) - 1. 4
 5, 76, 1065, 14840, 206701, 2878980, 40099025, 558507376, 7779004245, 108347552060, 1509086724601, 21018866592360, 292755045568445, 4077551771365876, 56792969753553825, 791024024778387680, 11017543377143873701, 153454583255235844140, 2137346622196157944265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also integers n such that n^2+(n+1)^2 is equal to the sum of two consecutive octagonal numbers. - Colin Barker, Dec 20 2014 REFERENCES Mario Velucchi, "Seeing couples", Recreational and Educational Computing, to appear 1997. [apparently never materialized, Joerg Arndt, Aug 14 2013] LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (15,-15,1). FORMULA a(n) = +15*a(n-1) -15*a(n-2) +a(n-3). G.f.: -x*(5+x)/ ((x-1) * (x^2-14*x+1)). - R. J. Mathar, Apr 15 2010 a(n) = (A007655(n+2) - 3*A007655(n+1) - 1)/2. - Ralf Stephan, Aug 13 2013 a(n) = (-6-(7-4*sqrt(3))^n*(-3+sqrt(3))+(3+sqrt(3))*(7+4*sqrt(3))^n)/12. - Colin Barker, Mar 05 2016 MATHEMATICA CoefficientList[Series[-(5 + x) / ((x - 1) (x^2 - 14 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 13 2013 *) PROG (PARI) Vec(-x*(5+x)/((x-1)*(x^2-14*x+1)) + O(x^100)) \\ Colin Barker, Dec 20 2014 CROSSREFS Cf. A011916. Sequence in context: A051481 A277296 A364323 * A209095 A136300 A196689 Adjacent sequences: A011915 A011916 A011917 * A011919 A011920 A011921 KEYWORD nonn,easy AUTHOR Mario Velucchi (mathchess(AT)velucchi.it) EXTENSIONS More terms from R. J. Mathar, Apr 15 2010 STATUS approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)