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A257713
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Triangular numbers (A000217) that are the sum of ten consecutive triangular numbers.
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6
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1485, 7260, 28920, 142845, 2112540, 10440165, 41673885, 205953660, 3046252485, 15054681960, 60093684540, 296985006165, 4392693942120, 21708840917445, 86655051404085, 428252172907560, 6334261618255845, 31304133548245020, 124956524030977320, 617539336347666645
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OFFSET
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1,1
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1442,-1442,0,0,-1,1).
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FORMULA
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G.f.: -15*x*(8*x^8-5*x^7+5*x^5-11445*x^4+7595*x^3+1444*x^2+385*x+99) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)*(x^4+38*x^2+1)).
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EXAMPLE
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1485 is in the sequence because T(54) = 1485 = 78+91+105+120+136+153+171+190+210+231 = T(12)+ ... +T(21).
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 1442, -1442, 0, 0, -1, 1}, {1485, 7260, 28920, 142845, 2112540, 10440165, 41673885, 205953660, 3046252485}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
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PROG
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(PARI) Vec(-15*x*(8*x^8-5*x^7+5*x^5-11445*x^4+7595*x^3+1444*x^2+385*x+99) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)*(x^4+38*x^2+1)) + O(x^100))
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CROSSREFS
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Cf. A000217, A001110, A129803, A131557, A257711, A257712, A259413, A259414, A259415.
Sequence in context: A137366 A045008 A327880 * A269923 A288075 A104742
Adjacent sequences: A257710 A257711 A257712 * A257714 A257715 A257716
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KEYWORD
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nonn
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AUTHOR
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Colin Barker, May 05 2015
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STATUS
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approved
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