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A257707
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Numbers n such that T(n) + T(n+1) + ... + T(n+22) is a square, where T = A000217 (triangular numbers).
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4
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56, 470, 1094, 7856, 128534, 201539, 3293081, 23435699, 53805155, 382911281, 6256309475, 9809462822, 160274811896, 1140616029542, 2618697452438, 18636292598096, 304494582579398, 477426555904883, 7800575092244921, 55513782134933123, 127452004956911987
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OFFSET
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1,1
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COMMENTS
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Positive integers y in the solutions to 2*x^2-23*y^2-529*y-4048 = 0.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,48670,-48670,0,0,0,0,-1,1).
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FORMULA
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G.f.: x*(10*x^12 +3*x^11 +66*x^10 +414*x^9 +624*x^8 +6762*x^7 -366022*x^6 -73005*x^5 -120678*x^4 -6762*x^3 -624*x^2 -414*x -56) / ((x -1)*(x^12 -48670*x^6 +1)).
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 0, 0, 48670, -48670, 0, 0, 0, 0, -1, 1}, {56, 470, 1094, 7856, 128534, 201539, 3293081, 23435699, 53805155, 382911281, 6256309475, 9809462822, 160274811896}, 50] (* Vincenzo Librandi, May 05 2015 *)
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PROG
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(PARI) Vec(x*(10*x^12 +3*x^11 +66*x^10 +414*x^9 +624*x^8 +6762*x^7 -366022*x^6 -73005*x^5 -120678*x^4 -6762*x^3 -624*x^2 -414*x -56) / ((x -1)*(x^12 -48670*x^6 +1)) + O(x^100))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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