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A027602
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n^3 + (n+1)^3 + (n+2)^3.
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9
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(3) = 216 = 6^3 (a cube). [From 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] - [From Joerg Arndt, Jan 25 2011]
Sums of three consecutive cubes. [From Al Hakanson (hawkuu(AT)gmail.com), May 20 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..750
P. De Geest, Palindromic Sums of Cubes of Consecutive Integers
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n) = +4*a(n-1)-6*a(n-2)+4*a(n-3)-1*a(n-4) for n>=4
a(n)=9*A006527(n+1). - Lekraj Beedassy (blekraj(AT)yahoo.com), Feb 01 2007
a(n) = 3*n^3 + 9*n^2 + 15*n + 9
G.f.: 9*(1+x^2)/(1-x)^4. a(n)=A008585(n+1)*A059100(n+1). - Bruno Berselli, Jan 21 2011
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MATHEMATICA
| f[n_]:=n^3; Table[f[n]+f[n+1]+f[n+2], {n, 0, 100}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
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PROG
| (Sage) [i^3+(i+1)^3+(i+2)^3 for i in xrange(0, 48)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
(MAGMA) [3*n^3 + 9*n^2 + 15*n + 9: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011
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CROSSREFS
| Cf. A003215, A000537, A000578, A005898 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 03 2009]
Sequence in context: A022604 A085630 A133226 * A134537 A066647 A187607
Adjacent sequences: A027599 A027600 A027601 * A027603 A027604 A027605
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KEYWORD
| nonn
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com)
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