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A259157
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Positive triangular numbers (A000217) that are hexagonal numbers (A000384) divided by 2.
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3
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3, 3570, 4119885, 4754343828, 5486508657735, 6331426236682470, 7306460390622912753, 8431648959352604634600, 9730115592632515125415755, 11228544962248963102125146778, 12957731156319710787337293966165, 14953210525847983999624135111807740
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OFFSET
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1,1
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COMMENTS
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Intersection of A000217 and A033991 (even hexagonal numbers divided by 2). - Michel Marcus, Jun 20 2015
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..327
Index entries for linear recurrences with constant coefficients, signature (1155,-1155,1).
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FORMULA
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G.f.: -3*x*(35*x+1) / ((x-1)*(x^2-1154*x+1)).
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EXAMPLE
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3 is in the sequence because 3 is the 2nd triangular number, and 2*3 is the 2nd hexagonal number.
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MATHEMATICA
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LinearRecurrence[{1155, -1155, 1}, {3, 3570, 4119885}, 20] (* Vincenzo Librandi, Jun 20 2015 *)
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PROG
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(PARI) Vec(-3*x*(35*x+1)/((x-1)*(x^2-1154*x+1)) + O(x^20))
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CROSSREFS
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Cf. A000217, A000384, A033991, A259156, A259158-A259167.
Sequence in context: A193447 A134909 A286215 * A003831 A200735 A226984
Adjacent sequences: A259154 A259155 A259156 * A259158 A259159 A259160
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Jun 19 2015
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STATUS
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approved
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