A034857 a(n) = C(n+2,3) + 2*C(n,2) + 2*(n-2).

-1, 6, 18, 36, 61, 94, 136, 188, 251, 326, 414, 516, 633, 766, 916, 1084, 1271, 1478, 1706, 1956, 2229, 2526, 2848, 3196, 3571, 3974, 4406, 4868, 5361, 5886, 6444, 7036, 7663, 8326, 9026, 9764, 10541, 11358, 12216, 13116, 14059, 15046, 16078, 17156, 18281, 19454, 20676

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[(n^3 + 9*n^2 + 8*n - 24)/6: n in [1..40]] // Vincenzo Librandi, Sep 09 2012

Mathematica

Table[(n^3 + 9n^2 + 8n - 24)/6,{n, 1, 60}] (* Vincenzo Librandi, Sep 09 2012 *)
LinearRecurrence[{4,-6,4,-1},{-1,6,18,36},50] (* Harvey P. Dale, Aug 10 2023 *)

PARI

for(n=1,50, print1((n^3+9*n^2+8*n-24)/6, ", ")) \\ G. C. Greubel, Feb 22 2018

Formula

a(n) = (n^3 + 9n^2 + 8n - 24)/6. - Ralf Stephan, Feb 15 2004

From Colin Barker, Sep 09 2012: (Start)

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

G.f.: x*(-1 +10*x -12*x^2 +4*x^3)/(1- x)^4. (End)