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A274588
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Values of n such that 2*n-1 and 7*n-1 are both triangular numbers.
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2
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1, 8, 638, 6931, 572671, 6223778, 514257668, 5588945461, 461802812941, 5018866799948, 414698411763098, 4506936797407591, 372398711960448811, 4047224225205216518, 334413628642071268928, 3634402847297487025321, 300303066121868039048281
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: (1+7*x-268*x^2+7*x^3+x^4) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).
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EXAMPLE
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8 is in the sequence because 2*8-1 = 15, 7*8-1 = 55, and 15 and 55 are both triangular numbers.
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MATHEMATICA
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CoefficientList[Series[(1 + 7 x - 268 x^2 + 7 x^3 + x^4)/((1 - x) (1 - 30 x + x^2) (1 + 30 x + x^2)), {x, 0, 16}], x] (* Michael De Vlieger, Jun 30 2016 *)
LinearRecurrence[{1, 898, -898, -1, 1}, {1, 8, 638, 6931, 572671}, 20] (* Harvey P. Dale, Apr 10 2023 *)
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PROG
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(PARI) isok(n) = ispolygonal(2*n-1, 3) && ispolygonal(7*n-1, 3)
(PARI) Vec((1+7*x-268*x^2+7*x^3+x^4)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20))
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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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