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A114040
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a(0) = 1, a(1) = 9, a(n) = 6*a(n-1) - a(n-2) - 4.
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0
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1, 9, 49, 281, 1633, 9513, 55441, 323129, 1883329, 10976841, 63977713, 372889433, 2173358881, 12667263849, 73830224209, 430314081401, 2508054264193, 14618011503753, 85200014758321, 496582077046169, 2894292447518689, 16869172608065961, 98320743200877073
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OFFSET
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0,2
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COMMENTS
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The most straightforward test for "triangularity" is istriangle(n) <===> issquare(8*n+1). If this sequence could be proved to be free of squares beyond the first three terms, that would lead directly to a proof that 0, 1 and 6 are the only triangular numbers whose squares are triangular numbers.
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LINKS
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FORMULA
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G.f.: (1+2x-7x^2)/((1-x)(1-6x+x^2)). [R. J. Mathar, Sep 09 2008]
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MATHEMATICA
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LinearRecurrence[{7, -7, 1}, {1, 9, 49}, 30] (* Harvey P. Dale, Aug 18 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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