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A048396
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Sums of consecutive noncubes.
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5
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0, 27, 315, 1638, 5670, 15345, 35217, 71820, 134028, 233415, 384615, 605682, 918450, 1348893, 1927485, 2689560, 3675672, 4931955, 6510483, 8469630, 10874430, 13796937, 17316585, 21520548, 26504100, 32370975, 39233727, 47214090, 56443338, 67062645, 79223445
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OFFSET
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0,2
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COMMENTS
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Relation with triangular numbers: a(n) = 3*((n^3+1) + ((n+1)^3-1)) * A000217(n). Example: a(3) = 3*(first term + last term)*A000217(3) = 3*(28+63)*6 = 1638.
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LINKS
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FORMULA
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a(n) = ( 6n^5 + 15n^4 + 18n^3 + 12n^2 + 3n ) / 2.
G.f.: 9*x*(1+x)*(3+14*x+3*x^2)/(1-x)^6. - Colin Barker, Mar 15 2012
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Wesley Ivan Hurt, Apr 10 2015
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EXAMPLE
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Between 3^3 and 4^3 we have: 28 + 29 + ... + 62 + 63 = 1638 = a(3).
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MAPLE
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MATHEMATICA
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Table[Total[Range[n^3+1, (n+1)^3-1]], {n, 0, 30}] (* Harvey P. Dale, Jan 08 2011 *)
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PROG
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(Magma) [(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2 : n in [0..50]]; // Wesley Ivan Hurt, Apr 10 2015
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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