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A254855
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Indices of octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).
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3
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1, 2, 16, 43, 407, 1108, 10558, 28757, 274093, 746566, 7115852, 19381951, 184738051, 503184152, 4796073466, 13063405993, 124513172057, 339145371658, 3232546400008, 8804716257107, 83921693228143, 228583477313116, 2178731477531702, 5934365693883901
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OFFSET
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1,2
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COMMENTS
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Also positive integers x in the solutions to 6*x^2 - 7*y^2 - 4*x + 7*y - 2 = 0, the corresponding values of y being A254856.
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LINKS
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FORMULA
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a(n) = a(n-1)+26*a(n-2)-26*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+x^3-12*x^2+x+1) / ((x-1)*(x^4-26*x^2+1)).
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EXAMPLE
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16 is in the sequence because the 16th octagonal number is 736, which is also the 15th centered heptagonal number.
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MATHEMATICA
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LinearRecurrence[{1, 26, -26, -1, 1}, {1, 2, 16, 43, 407}, 30] (* Harvey P. Dale, Aug 31 2021 *)
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PROG
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(PARI) Vec(-x*(x^4+x^3-12*x^2+x+1)/((x-1)*(x^4-26*x^2+1)) + O(x^100))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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