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A254856
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Indices of centered heptagonal numbers (A069099) that are also octagonal numbers (A000567).
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3
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1, 2, 15, 40, 377, 1026, 9775, 26624, 253761, 691186, 6587999, 17944200, 171034201, 465858002, 4440301215, 12094363840, 115276797377, 313987601826, 2992756430575, 8151583283624, 77696390397561, 211627177772386, 2017113393905999, 5494155038798400
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OFFSET
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1,2
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COMMENTS
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Also positive integers y in the solutions to 6*x^2 - 7*y^2 - 4*x + 7*y - 2 = 0, the corresponding values of x being A254855.
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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^3+13*x^2-x-1) / ((x-1)*(x^4-26*x^2+1)).
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EXAMPLE
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15 is in the sequence because the 15th centered heptagonal number is 736, which is also the 16th octagonal number.
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MATHEMATICA
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LinearRecurrence[{1, 26, -26, -1, 1}, {1, 2, 15, 40, 377}, 30] (* Harvey P. Dale, Apr 30 2019 *)
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PROG
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(PARI) Vec(x*(x^3+13*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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