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A259415
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Triangular numbers (A000217) that are the sum of seventeen consecutive triangular numbers.
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6
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1326, 9180, 24531, 1979055, 5325216, 39529386, 106368405, 8616365901, 23185550130, 172110498456, 463127571831, 37515654714891, 100949879501796, 749369070309030, 2016457340944761, 163343152011830505, 439535752164830646, 3262752760014579156
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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 (1,0,0,4354,-4354,0,0,-1,1).
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FORMULA
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G.f.: -51*x*(11*x^8 +15*x^6 +154*x^5 -47593*x^4 +38324*x^3 +301*x^2 +154*x +26) / ((x -1)*(x^2 -8*x -1)*(x^2 +8*x -1)*(x^4 +66*x^2 +1)).
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EXAMPLE
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1326 is in the sequence because T(51) = 1326 = 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 + 91 + 105 + 120 + 136 + 153 + 171 + 190 = T(3) + ... + T(19).
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 4354, -4354, 0, 0, -1, 1}, {1326, 9180, 24531, 1979055, 5325216, 39529386, 106368405, 8616365901, 23185550130}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
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PROG
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(PARI) Vec(-51*x*(11*x^8 +15*x^6 +154*x^5 -47593*x^4 +38324*x^3 +301*x^2 +154*x +26) / ((x -1)*(x^2 -8*x -1)*(x^2 +8*x -1)*(x^4 +66*x^2 +1)) + O(x^30))
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CROSSREFS
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Cf. A000217, A001110, A129803, A131557, A257711, A257712, A257713, A259413, A259414.
Sequence in context: A249080 A248984 A202374 * A015162 A075037 A134116
Adjacent sequences: A259412 A259413 A259414 * A259416 A259417 A259418
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Jun 26 2015
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STATUS
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approved
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