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A027603
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a(n) = n^3 + (n+1)^3 + (n+2)^3 + (n+3)^3.
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5
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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;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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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) -a(n-4) for n>=4.
a(n) = 4*n^3 + 18*n^2 + 42*n + 36 = 4*A173965(n+2).
G.f.: 4*(9 - 11*x + 10*x^2 - 2*x^3)/(1-x)^4.
E.g.f.: 2*(18 + 32*x + 15*x^2 + 2*x^3)*exp(x). - G. C. Greubel, Aug 24 2022
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MAPLE
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MATHEMATICA
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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}] (* Alonso del Arte, Jan 24 2011 *)
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PROG
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(Sage) [n^3+(n+1)^3+(n+2)^3+(n+3)^3 for n in range(0, 40)] # Zerinvary Lajos, Jul 03 2008
(Magma) [4*n^3 + 18*n^2 + 42*n + 36: n in [0..40]]; // Vincenzo Librandi, Jun 04 2011
(Python)
A027603_list, m = [], [24, 12, 28, 36]
for _ in range(10**2):
for i in range(3):
(PARI) Vec(-4*(-9+11*x-10*x^2+2*x^3)/(1-x)^4 + O(x^100)) \\ Altug Alkan, Dec 16 2015
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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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