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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
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OFFSET
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1,1
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COMMENTS
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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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LINKS
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FORMULA
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a(2n-1) = 2*(2n-1)*(2n^2 -2n +1), a(2n) = 3*n*(4n^2 +1).
G.f.: x*(2+15*x+22*x^2+42*x^3+22*x^4+15*x^5+2*x^6) / ( (x-1)^4*(1+x)^4 ). - R. J. Mathar, Mar 21 2016
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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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EXTENSIONS
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STATUS
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approved
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