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A027603
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n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3.
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1
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36, 100, 224, 432, 748, 1196, 1800, 2584, 3572, 4788, 6256, 8000, 10044, 12412, 15128, 18216, 21700, 25604, 29952, 34768, 40076, 45900, 52264, 59192, 66708, 74836, 83600, 93024, 103132, 113948, 125496, 137800, 150884, 164772
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Sums of four 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..1000
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) = 4*n^3 + 18*n^2 + 42*n + 36.
G.f.: -4*(-9+11*x-10*x^2+2*x^3)/(1-x)^4. a(n)=A027689(n+1)*A016825(n+1). - Bruno Berselli, Jan 24 2011
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MATHEMATICA
| Table[n^3 + (n + 1)^3 + (n + 2)^3 + (n + 3)^3, {n, 0, 33}]
(* or *)
Table[Plus@@(Range[n, n + 3]^3), {n, 0, 33}] (* From Alonso del Arte, Jan 24 2011 *)
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PROG
| (Sage) [n^3+(n+1)^3+(n+2)^3+(n+3)^3 for n in xrange(0, 40)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
(MAGMA) [4*n^3 + 18*n^2 + 42*n + 36: n in [0..40]]; // Vincenzo Librandi, Jun 04 2011
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CROSSREFS
| Cf. A173965.
Sequence in context: A177492 A077448 A085986 * A163246 A014738 A182677
Adjacent sequences: A027600 A027601 A027602 * A027604 A027605 A027606
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KEYWORD
| nonn
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com)
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