A152064 a(n) = 2*n^3 - 3*n^2 + 5.

5, 4, 9, 32, 85, 180, 329, 544, 837, 1220, 1705, 2304, 3029, 3892, 4905, 6080, 7429, 8964, 10697, 12640, 14805, 17204, 19849, 22752, 25925, 29380, 33129, 37184, 41557, 46260, 51305, 56704, 62469, 68612, 75145, 82080, 89429, 97204, 105417, 114080, 123205

Offset: 0

Author

Paul Curtz, Nov 23 2008

Keywords

• nonn
• easy

References

• P. Curtz, Integration numerique des systemes differentiels a conditions initiales, 135 pages, Centre de Calcul Scientifique de l'Armement, Arcueil, 1969.

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

[2*n^3-3*n^2+5: n in [0..40]]; // Vincenzo Librandi, Aug 07 2011

Mathematica

Table[2n^3-3n^2+5,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{5,4,9,32},50] (* Harvey P. Dale, Oct 12 2012 *)

PARI

a(n)=2*n^3-3*n^2+5 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 12.

G.f.: ( 5 - 16*x + 23*x^2 ) / (x-1)^4. - R. J. Mathar, Jul 06 2011

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=5, a(1)=4, a(2)=9, a(3)=32. - Harvey P. Dale, Oct 12 2012

Extensions

Simpler definition and more terms from Paolo P. Lava, Nov 27 2008

Edited by N. J. A. Sloane, Jan 04 2008