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A084990
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n*(n^2+3*n-1)/3.
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6
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0, 1, 6, 17, 36, 65, 106, 161, 232, 321, 430, 561, 716, 897, 1106, 1345, 1616, 1921, 2262, 2641, 3060, 3521, 4026, 4577, 5176, 5825, 6526, 7281, 8092, 8961, 9890, 10881, 11936, 13057, 14246, 15505, 16836, 18241, 19722, 21281, 22920, 24641, 26446, 28337, 30316
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = A077415(n+1) + 1 for n>0; a(n) = A000290(n) + A007290(n); a(n+1) = Sum(A028387(k): 0<=k<=n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007
a(n) is the number of triples (x,y,z) in {1,2,..,n}^3 with x <= y <= z or x >= y >= z. - Jack Kennedy, Mar 14 2009
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FORMULA
| Row sums of triangle A131782 starting (1, 6, 17, 36, 65, 106,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 14 2007
a(n) = (n-1)*(n+1)*(n+3)/3 + 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007
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MATHEMATICA
| Table[n*(n^2+3*n-1)/3, {n, 0, 6!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 08 2010]
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CROSSREFS
| a(n)=2*A000292(n-1)-1 (notice offset=-1 in A000292!)
Cf. A131782.
Sequence in context: A038633 A083045 A012277 * A024181 A023663 A048208
Adjacent sequences: A084987 A084988 A084989 * A084991 A084992 A084993
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KEYWORD
| nonn
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AUTHOR
| Gary Adamson, Jul 16 2003
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