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A146298
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Difference between the cubes and 2*Tetrahedral numbers; A000578(n) - 2*A000292(n).
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n) = (n-2)*n*(2n+1)/3.
G.f.: x*(-1+4*x+x^2)/(1-x)^4. [From R. J. Mathar, Oct 31 2008]
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EXAMPLE
| a(4)=(4-2)*4*(2*4+1)/3 = 2*4*3 = 24
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MATHEMATICA
| Table[(n-2)*n*(2*n+1)/3, {n, 0, 30}]
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PROG
| (Other) 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]
(MAGMA) A000578:=func< n | n^3 >; A000292:=func< n | n*(n+1)*(n+2)/6 >; [ A000578(n)-2*A000292(n): n in [0..30] ]; // Bruno Berselli, Apr 07 2011
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CROSSREFS
| Cf. A000292, A000578.
Sequence in context: A196116 A168668 A159225 * A079671 A100454 A081436
Adjacent sequences: A146295 A146296 A146297 * A146299 A146300 A146301
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KEYWORD
| sign,easy
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AUTHOR
| J. Perry (johnandruth(AT)jrperry.orangehome.co.uk), Oct 29 2008
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EXTENSIONS
| Edited by Bruno Berselli, Apr 07 2011
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