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A253878
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Indices of triangular numbers (A000217) which are also centered heptagonal numbers (A069099).
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3
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1, 22, 358, 5713, 91057, 1451206, 23128246, 368600737, 5874483553, 93623136118, 1492095694342, 23779907973361, 378986431879441, 6040003002097702, 96261061601683798, 1534136982624843073, 24449930660395805377, 389664753583708042966, 6210186126678932882086
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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 x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of y being A253879.
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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*(x^2+5*x+1) / ((x-1)*(x^2-16*x+1)).
a(n) = (-2+(8-3*sqrt(7))^n*(3+sqrt(7))-(-3+sqrt(7))*(8+3*sqrt(7))^n)/4. - Colin Barker, Mar 04 2016
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EXAMPLE
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22 is in the sequence because the 22nd triangular number is 253, which is also the 9th centered heptagonal number.
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PROG
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(PARI) Vec(-x*(x^2+5*x+1)/((x-1)*(x^2-16*x+1)) + O(x^100))
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CROSSREFS
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Cf. A000217, A069099, A253879, A253880.
Sequence in context: A016263 A001718 A199671 * A081127 A016196 A238318
Adjacent sequences: A253875 A253876 A253877 * A253879 A253880 A253881
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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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