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A133273
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Indices of centered decagonal numbers which are also decagonal numbers.
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3
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1, 10, 171, 3060, 54901, 985150, 17677791, 317215080, 5692193641, 102142270450, 1832868674451, 32889493869660, 590178020979421, 10590314883759910, 190035489886698951, 3410048503076821200, 61190837565496082641, 1098025027675852666330, 19703259660599851911291
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OFFSET
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1,2
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COMMENTS
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Numbers k such that 80*k^2 - 80*k + 25 is a square.
Also the indices of centered square numbers which are also centered pentagonal numbers. - Colin Barker, Jan 01 2015
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LINKS
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FORMULA
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a(n+2) = 18*a(n+1) - a(n) - 8.
a(n+1) = 9*a(n) - 4 + sqrt(80*a(n)^2 - 80*a(n) + 25).
G.f.: x*(-1+9*x)/(-1+x)/(1 - 18*x + x^2). - R. J. Mathar, Nov 14 2007
a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3). - Colin Barker, Jan 01 2015
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MATHEMATICA
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LinearRecurrence[{19, -19, 1}, {1, 10, 171}, 20] (* Harvey P. Dale, Oct 09 2020 *)
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PROG
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(PARI) Vec(x*(-1+9*x)/((-1+x)*(1-18*x+x^2)) + O(x^100)) \\ Colin Barker, Jan 01 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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