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Search: id:A146298
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| 0, -1, 0, 7, 24, 55, 104, 175, 272, 399, 560, 759, 1000, 1287, 1624, 2015, 2464, 2975, 3552, 4199, 4920, 5719, 6600, 7567, 8624, 9775, 11024, 12375, 13832, 15399, 17080
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OFFSET
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0,4
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COMMENT
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Can be visualized as layering a cube up from a corner. Eventually the series of triangular numbers is truncated. So 7 = 10-3 (the corners are removed), 24 = 15+15-3-3 and 55 = 21+28+21-3-9-3.
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FORMULA
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a(n) = (n-2).n.(2n+1)/3
G.f.: x(-1+4x+x^2)/(1-x)^4. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 31 2008]
G.f.: sage: taylor( mul( x*(x^2+4*x-1)/(x-1)^4 for i in xrange(1,2)),x,0,30)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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EXAMPLE
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a(4)=(4-2).4.(2.4+1)/3 = 2.4.3 = 24
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MATHEMATICA
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Table[(n-2)*n*(2*n+1)/3, {n, 0, 30}]
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CROSSREFS
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Cf. A000292, A000578
Sequence in context: A031306 A006707 A159225 this_sequence A079671 A100454 A081436
Adjacent sequences: A146295 A146296 A146297 this_sequence A146299 A146300 A146301
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KEYWORD
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sign
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AUTHOR
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J. Perry (johnandruth(AT)jrperry.orangehome.co.uk), Oct 29 2008
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