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A253457
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Indices of centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).
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3
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1, 14, 351, 9100, 236237, 6133050, 159223051, 4133666264, 107316099801, 2786084928550, 72330892042487, 1877817108176100, 48750913920536101, 1265645944825762514, 32858043651549289251, 853043488995455758000, 22146272670230300418737, 574950045936992355129150
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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 - 6*x + 7*y = 0, the corresponding values of y being A253458.
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LINKS
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FORMULA
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a(n) = 27*a(n-1)-27*a(n-2)+a(n-3).
G.f.: x*(13*x-1) / ((x-1)*(x^2-26*x+1)).
a(n) = sqrt((-2-(13-2*sqrt(42))^n-(13+2*sqrt(42))^n)*(2-(13-2*sqrt(42))^(1+n)-(13+2*sqrt(42))^(1+n)))/(4*sqrt(6)). - Gerry Martens, Jun 04 2015
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EXAMPLE
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14 is in the sequence because the 14th centered hexagonal number is 547, which is also the 13th centered heptagonal number.
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PROG
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(PARI) Vec(x*(13*x-1)/((x-1)*(x^2-26*x+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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