A027444 a(n) = n^3 + n^2 + n.

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

Offset: 0

Author

Patrick De Geest and Mark Milhet (mm992395(AT)shellus.com)

Keywords

• nonn
• easy

Comments

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

Examples

			For n = 4, 4^3 + 4^2 + 4 = 64 + 16 + 4 = 84.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• D. Applegate, M. LeBrun, and 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 Circles.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Column k=3 of A228275.

Cf. A270109.

Programs

Magma

[n^3 + n^2 + n: n in [0..50]]; // Vincenzo Librandi, Jun 09 2011

Maple

A027444:=n->n^3+n^2+n: seq(A027444(n), n=0..100); # Wesley Ivan Hurt, Apr 05 2016

Mathematica

Table[n^3 + n^2 + n, {n, 0, 50}] (* Harvey P. Dale, Dec 13 2013 *)

Formula

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