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A253879
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Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217).
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3
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1, 9, 136, 2160, 34417, 548505, 8741656, 139317984, 2220346081, 35386219305, 563959162792, 8987960385360, 143243407002961, 2282906551662009, 36383261419589176, 579849276161764800, 9241205157168647617, 147279433238536597065, 2347229726659416905416
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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 x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of x being A253878.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..832
Index entries for linear recurrences with constant coefficients, signature (17,-17,1).
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FORMULA
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a(n) = 17*a(n-1)-17*a(n-2)+a(n-3).
G.f.: x*(8*x-1) / ((x-1)*(x^2-16*x+1)).
a(n) = (14-(8-3*sqrt(7))^n*(7+3*sqrt(7))+(-7+3*sqrt(7))*(8+3*sqrt(7))^n)/28. - Colin Barker, Mar 04 2016
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EXAMPLE
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9 is in the sequence because the 9th centered heptagonal number is 253, which is also the 22nd triangular number.
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PROG
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(PARI) Vec(x*(8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^100))
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CROSSREFS
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Cf. A000217, A069099, A253878, A253880.
Sequence in context: A188685 A052137 A003376 * A309189 A231757 A156975
Adjacent sequences: A253876 A253877 A253878 * A253880 A253881 A253882
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Jan 17 2015
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STATUS
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approved
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