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A027444
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a(n) = n^3 + n^2 + n.
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22
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0, 3, 14, 39, 84, 155, 258, 399, 584, 819, 1110, 1463, 1884, 2379, 2954, 3615, 4368, 5219, 6174, 7239, 8420, 9723, 11154, 12719, 14424, 16275, 18278, 20439, 22764, 25259, 27930, 30783, 33824, 37059, 40494, 44135, 47988, 52059, 56354, 60879, 65640, 70643, 75894
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OFFSET
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0,2
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COMMENTS
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For n>1, a(n) is the volume of a truncated square pyramid with height n and base lengths n+2 and n-1. - Wesley Ivan Hurt, Apr 05 2016
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Eric Weisstein's World of Mathematics, Magic Circle - Eric W. Weisstein, Feb 06 2009
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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O.g.f.: x*(3 + 2*x + x^2)/(1 - x)^4. - R. J. Mathar, Feb 04 2008
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Wesley Ivan Hurt, Apr 05 2016
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EXAMPLE
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For n = 4, 4^3 + 4^2 + 4 = 64 + 16 + 4 = 84.
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MAPLE
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A027444:=n->n^3+n^2+n: seq(A027444(n), n=0..100); # Wesley Ivan Hurt, Apr 05 2016
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MATHEMATICA
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Table[n^3 + n^2 + n, {n, 0, 50}] (* Harvey P. Dale, Dec 13 2013 *)
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PROG
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(MAGMA) [n^3 + n^2 + n: n in [0..50]]; // Vincenzo Librandi, Jun 09 2011
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CROSSREFS
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Column k=3 of A228275.
Cf. A270109.
Sequence in context: A143941 A162147 A319791 * A000263 A102590 A174517
Adjacent sequences: A027441 A027442 A027443 * A027445 A027446 A027447
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest, Mark Milhet (mm992395(AT)shellus.com)
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STATUS
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approved
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