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A052276
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Nonnegative numbers of the form n^3 (+/-) 3, n >= 0.
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2
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3, 4, 5, 11, 24, 30, 61, 67, 122, 128, 213, 219, 340, 346, 509, 515, 726, 732, 997, 1003, 1328, 1334, 1725, 1731, 2194, 2200, 2741, 2747, 3372, 3378, 4093, 4099, 4910, 4916, 5829, 5835, 6856, 6862, 7997, 8003, 9258, 9264, 10645, 10651
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OFFSET
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1,1
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COMMENTS
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It is conjectured that A003325 and A052276 (the current sequence) have infinitely many numbers in common, although only one example (128) is known.
The next such example must be larger than 2*10^12. - M. F. Hasler, Jan 10 2021
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LINKS
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FORMULA
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a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7) for n>8. - Colin Barker, Jul 09 2015
G.f.: x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3) / ((x-1)^4*(x+1)^3). - Colin Barker, Jul 09 2015
a(n) = ((2*n+1)*(n^2+n+1) - (-1)^n*(3*n^2+3*n-47))/16 for n >= 2. - Robert Israel, Jul 09 2015
a(n) = ceiling(n/2)^3 + 3*(-1)^n for all n > 1. - M. F. Hasler, Jan 10 2021
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MAPLE
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3, 4, op(map(n -> (n^3-3, n^3+3), [$2..100])); # Robert Israel, Jul 09 2015
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PROG
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(PARI) Vec(x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Jul 09 2015
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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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