A270809 a(n) = n^3/3 - 7*n/3 + 4.

4, 2, 2, 6, 16, 34, 62, 102, 156, 226, 314, 422, 552, 706, 886, 1094, 1332, 1602, 1906, 2246, 2624, 3042, 3502, 4006, 4556, 5154, 5802, 6502, 7256, 8066, 8934, 9862, 10852, 11906, 13026, 14214, 15472, 16802, 18206, 19686, 21244, 22882, 24602, 26406, 28296, 30274

Offset: 0

Author

N. J. A. Sloane, Apr 06 2016

Keywords

• nonn
• easy

Links

• M. Diepenbroek, M. Maus, A. Stoll, Pattern Avoidance in Reverse Double Lists, Preprint 2015. See Theorem 3.14.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A105163.

Programs

Magma

[n^3/3-7*n/3+4: n in [0..50]]; // Vincenzo Librandi, Apr 08 2016

Mathematica

Table[n^3 / 3 - 7 n / 3 + 4, {n, 0, 50}] (* Vincenzo Librandi, Apr 08 2016 *)
LinearRecurrence[{4,-6,4,-1},{4,2,2,6},50] (* Harvey P. Dale, Jul 18 2025 *)

PARI

vector(50, n, n--; n^3/3-7*n/3+4) \\ Bruno Berselli, Apr 08 2016

PARI

x='x+O('x^99); Vec((4-14*x+18*x^2-6*x^3)/(1-x)^4) \\ Altug Alkan, Apr 08 2016

Sage

[n^3/3-7*n/3+4 for n in [0..50]] # Bruno Berselli, Apr 08 2016

Formula

O.g.f.: (4 - 14*x + 18*x^2 - 6*x^3)/(1-x)^4. - Vincenzo Librandi, Apr 08 2016

E.g.f.: (12 - 6*x + 3*x^2 + x^3)*exp(x)/3. - Bruno Berselli, Apr 08 2016

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - Vincenzo Librandi, Apr 08 2016

a(n) = 2*A105163(n) for n>0. - Bruno Berselli, Apr 08 2016