A006592 a(n) = 10*n^3 - 6*n^2.

0, 4, 56, 216, 544, 1100, 1944, 3136, 4736, 6804, 9400, 12584, 16416, 20956, 26264, 32400, 39424, 47396, 56376, 66424, 77600, 89964, 103576, 118496, 134784, 152500, 171704, 192456, 214816, 238844, 264600, 292144, 321536, 352836, 386104, 421400, 458784, 498316, 540056

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

References

• W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 29.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Programs

Magma

[10*n^3-6*n^2: n in [0..40]]; // Vincenzo Librandi, Jul 20 2011

Mathematica

Table[10n^3-6n^2,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,4,56,216},50] (* Harvey P. Dale, Aug 13 2012 *)

PARI

a(n)=10*n^3-6*n^2;

Formula

a(n) = 4 * A006597(n).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=4, a(2)=56, a(3)=216. - Harvey P. Dale, Aug 13 2012

From G. C. Greubel, Oct 18 2018: (Start)

G.f.: 4*(x + 10*x^2 + 4*x^3)/(1 - x)^4.

E.g.f.: 2*x*(2 + 12*x + 5*x^2)*exp(x). (End)

Extensions

Name corrected by Arkadiusz Wesolowski, Jul 20 2011