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A263947
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Positive integers n such that (n+57)^3 - n^3 is a square.
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8
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551, 13471, 67002512, 1560515752, 7745359676111, 180392503180711, 895348087775371352, 20853012581126608912, 103500448242912021166871, 2410566548172681237123151, 11964444815088795735075876992, 278656671814812593067838694872, 1383065891631134161140389210648831
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = a(n-1)+115598*a(n-2)-115598*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: 19*x*(32*x^4+680*x^3-173397*x^2-680*x-29) / ((x-1)*(x^2-340*x+1)*(x^2+340*x+1)).
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EXAMPLE
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551 is in the sequence because (551+57)^3 - 551^3 = 7581^2.
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MATHEMATICA
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LinearRecurrence[{1, 115598, -115598, -1, 1}, {551, 13471, 67002512, 1560515752, 7745359676111}, 15] (* Paolo Xausa, Mar 05 2024 *)
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PROG
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(PARI) Vec(19*x*(32*x^4+680*x^3-173397*x^2-680*x-29)/((x-1)*(x^2-340*x+1)*(x^2+340*x+1)) + 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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