A067389 a(n) = 3*n^3 + 2*n^2 + n.

0, 6, 34, 102, 228, 430, 726, 1134, 1672, 2358, 3210, 4246, 5484, 6942, 8638, 10590, 12816, 15334, 18162, 21318, 24820, 28686, 32934, 37582, 42648, 48150, 54106, 60534, 67452, 74878, 82830, 91326, 100384, 110022, 120258, 131110, 142596

Offset: 0

Author

George E. Antoniou, Jan 21 2002

Keywords

• nonn
• easy

Links

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

Programs

Magma

[3*n^3 + 2*n^2 + n: n in [0..60]]; // Vincenzo Librandi, May 08 2011

Maple

a:=n->n+2*n^2+3*n^3: seq(a(n), n=0..36); # Zerinvary Lajos, Oct 05 2007

Mathematica

Table[3*n^3+2*n^2+n,{n,0,80}] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)
LinearRecurrence[{4,-6,4,-1},{0,6,34,102},40] (* Harvey P. Dale, Oct 01 2019 *)

Formula

a(n) = n*A056109(n) = A045991(n+1)+A033431(n). - Henry Bottomley, Jan 25 2002

From Chai Wah Wu, Apr 25 2017: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.

G.f.: 2*x*(x^2 + 5*x + 3)/(x - 1)^4. (End)

Extensions

More terms from Henry Bottomley, Jan 25 2002