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 A253714 Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099). 3
 1, 2857, 45529, 184300369, 2937241777, 11889953986681, 189493215939721, 767068491312421537, 12224965330197902689, 49486656636639609035209, 788681413122894278122297, 3192582165489099245985035761, 50880992673985436128583949841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers x in the solutions to 4*x^2-7*y^2-2*x+7*y-2 = 0, the corresponding values of y being A253715. LINKS Colin Barker, Table of n, a(n) for n = 1..416 Index entries for linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1). FORMULA a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5). G.f.: -x*(x^4+2856*x^3-21842*x^2+2856*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)). EXAMPLE 2857 is in the sequence because the 2857th hexagonal number is 16322041, which is also the 2160th centered heptagonal number. PROG (PARI) Vec(-x*(x^4+2856*x^3-21842*x^2+2856*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100)) CROSSREFS Cf. A000384, A069099, A253715, A253716. Sequence in context: A233788 A250637 A067703 * A031603 A236586 A233379 Adjacent sequences: A253711 A253712 A253713 * A253715 A253716 A253717 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 10 2015 STATUS approved

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Last modified August 5 15:04 EDT 2024. Contains 374950 sequences. (Running on oeis4.)