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 A251769 Numbers n such that the sum of the heptagonal numbers H(n), H(n+1) and H(n+2) is equal to the sum of three consecutive squares. 2
 17, 239, 25529, 345647, 36813809, 498423743, 53085488057, 718726692767, 76549236965393, 1036403392547279, 110383946618609657, 1494492973326484559, 159173574474798161009, 2155057831133398187807, 229528184008712329566329, 3107591898001386860334143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also nonnegative integers x in the solutions to 15*x^2-6*y^2+21*x-12*y+6 = 0, the corresponding values of y being A251770. LINKS Colin Barker, Table of n, a(n) for n = 1..633 Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1). FORMULA a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5). G.f.: x*(x^4+6*x^3-776*x^2-222*x-17) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)). EXAMPLE 17 is in the sequence because H(17)+H(18)+H(19) = 697+783+874 = 2354 = 729+784+841 = 27^2+28^2+29^2. PROG (PARI) Vec(x*(x^4+6*x^3-776*x^2-222*x-17)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100)) CROSSREFS Cf. A000290, A000566, A251770. Sequence in context: A125474 A264455 A142126 * A290340 A103772 A196987 Adjacent sequences:  A251766 A251767 A251768 * A251770 A251771 A251772 KEYWORD nonn,easy AUTHOR Colin Barker, Dec 08 2014 STATUS approved

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Last modified February 22 05:52 EST 2020. Contains 332116 sequences. (Running on oeis4.)