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 A252985 Numbers n such that the sum of the hexagonal numbers X(n) and X(n+1) is equal to the heptagonal number H(m) for some m. 2
 1, 579, 1870, 835278, 2696899, 1204470657, 3888926848, 1736845852476, 5607829818277, 2504530514800095, 8086486709028946, 3611531265495884874, 11660708226589922215, 5207825580314551188573, 16814733176255958805444, 7509680875282317318037752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers x in the solutions to 8*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252986. 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*(68*x^3+151*x^2-578*x-1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)). EXAMPLE 1 is in the sequence because X(1)+X(2) = 1+6 = 7 = H(2). PROG (PARI) Vec(x*(68*x^3+151*x^2-578*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100)) CROSSREFS Cf. A000384, A000566, A252986. Sequence in context: A286233 A073735 A250727 * A097769 A186786 A185609 Adjacent sequences:  A252982 A252983 A252984 * A252986 A252987 A252988 KEYWORD nonn,easy AUTHOR Colin Barker, Dec 25 2014 STATUS approved

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Last modified May 26 01:21 EDT 2022. Contains 354073 sequences. (Running on oeis4.)