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A050492
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Thickened cube numbers: a(n) = n*(n^2 + (n-1)^2) + (n-1)*2*n*(n-1).
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7
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1, 14, 63, 172, 365, 666, 1099, 1688, 2457, 3430, 4631, 6084, 7813, 9842, 12195, 14896, 17969, 21438, 25327, 29660, 34461, 39754, 45563, 51912, 58825, 66326, 74439, 83188, 92597, 102690, 113491, 125024, 137313, 150382, 164255, 178956
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OFFSET
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1,2
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COMMENTS
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In other words, positive integers k such that 2*k - 1 is a perfect cube. - Altug Alkan, Apr 15 2016
a(n) represents the first term in a sum of (2*n - 1)^3 consecutive integers which equals (2*n - 1)^6. - Patrick J. McNab, Dec 24 2016
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LINKS
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FORMULA
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a(n) = n*(4*n^2-6*n+3).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=14, a(3)=63, a(4)=172. - Harvey P. Dale, Oct 02 2011
G.f.: x*(1+10*x+13*x^2)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 04 2012
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EXAMPLE
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* * * * *
a(2) = * + * * + * = 14.
* * * * *
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MATHEMATICA
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Table[n(n^2+(n-1)^2)+(n-1)2n(n-1), {n, 40}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 14, 63, 172}, 40] (* Harvey P. Dale, Oct 02 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999
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STATUS
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approved
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