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A133272
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Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).
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3
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1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543
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OFFSET
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1,2
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COMMENTS
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Numbers X such that 140*X^2-140*X+49 is a square.
Also positive integers x in the solutions to 5*x^2 - 7*y^2 - 5*x + 7*y = 0, the corresponding values of y being A253621. - Colin Barker, Jan 06 2015
Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - Colin Barker, Jan 06 2015
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LINKS
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FORMULA
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a(n+2) = 12*a(n+1) - a(n) - 5.
a(n+1) = 6*a(n) - 5/2 + (1/2)*sqrt(140*a(n)^2 - 140*a(n) + 49).
G.f.: x*(-1+6*x)/((-1+x)*(1-12*x+x^2)). - R. J. Mathar, Nov 14 2007
a(n) = 13*a(n-1) - 13*a(n-2) + a(n-3). - Colin Barker, Jan 06 2015
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MATHEMATICA
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LinearRecurrence[{13, -13, 1}, {1, 7, 78}, 25] (* Paolo Xausa, Jan 07 2024 *)
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PROG
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(PARI) Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ Colin Barker, Jan 06 2015
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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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EXTENSIONS
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STATUS
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approved
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