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A027602
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a(n) = n^3 + (n+1)^3 + (n+2)^3.
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13
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9, 36, 99, 216, 405, 684, 1071, 1584, 2241, 3060, 4059, 5256, 6669, 8316, 10215, 12384, 14841, 17604, 20691, 24120, 27909, 32076, 36639, 41616, 47025, 52884, 59211, 66024, 73341, 81180, 89559, 98496, 108009, 118116, 128835, 140184
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OFFSET
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0,1
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COMMENTS
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a(3) = 216 = 6^3 (a cube). - Howard Berman (howard_berman(AT)hotmail.com), Nov 07 2008
Pairs [n,a(n)] for n<=10^7 such that a(n) is a perfect power are [0, 9], [1, 36], [3, 216], [23, 41616]. - Joerg Arndt, Jan 25 2011
Sums of three consecutive cubes. - Al Hakanson (hawkuu(AT)gmail.com), May 20 2009
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 1*a(n-4) for n>=4.
a(n) = 3*n^3 + 9*n^2 + 15*n + 9.
E.g.f.: 3*(3 + 9*x + 6*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 24 2022
Sum_{n>=0} 1/a(n) = (2*gamma + polygamma(0, 1-i*sqrt(2)) + polygamma(0, 1+i*sqrt(2))/12 = 0.161383557127191633050394086192620963436504... where i denotes the imaginary unit. - Stefano Spezia, Aug 31 2023
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MATHEMATICA
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PROG
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(Sage) [i^3+(i+1)^3+(i+2)^3 for i in range(0, 48)] # Zerinvary Lajos, Jul 03 2008
(Python)
A027602_list, m = [], [18, 0, 9, 9]
for _ in range(10**2):
for i in range(3):
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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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STATUS
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approved
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