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A093917
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a(n)=n^3+n for odd n, (n^3+n)*3/2 for even n: Row sums of A093915.
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3
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2, 15, 30, 102, 130, 333, 350, 780, 738, 1515, 1342, 2610, 2210, 4137, 3390, 6168, 4930, 8775, 6878, 12030, 9282, 16005, 12190, 20772, 15650, 26403, 19710, 32970, 24418, 40545, 29822, 49200, 35970, 59007, 42910, 70038, 50690, 82365, 59358
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Initially defined as sum of the n-th row of the triangle A093915, constructed by trial and error. Namely, this row should contain n consecutive integers [x,x+1,...,x+n-1], listed in A093915, and have its sum a(n) = n*x+n(n-1)/2 equal to the least possible strict (>1) multiple of the sum of the indices of these elements in A093915, which equals A006003(n) = (n^3+n)/2. For odd n, a(n) = 2 A006003(n) is obtained for x = A093916(n). For even n, the sum a(n) cannot equal 2 A006003(n), but it does equal 3 A006003(n) for x = A093916(n). Hence this simple explicit definition of a(n). - M. F. Hasler, Apr 04 2009
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FORMULA
| a(n) = n*A093916(n)+n(n-1)/2. - M. F. Hasler, Apr 04 2009
a(2n-1) = 2*(2n-1)*(2n^2 -2n +1), a(2n) = 3*n*(4n^2 +1)
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CROSSREFS
| Cf. A093915, A093916, A093918.
Sequence in context: A032002 A071999 A031289 * A076352 A154790 A042461
Adjacent sequences: A093914 A093915 A093916 * A093918 A093919 A093920
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 25 2004
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EXTENSIONS
| More terms from Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Jul 25 2006
Edited by M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 04 2009
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