A106058 4th diagonal of triangle in A059317.

0, 0, 0, 2, 9, 22, 42, 70, 107, 154, 212, 282, 365, 462, 574, 702, 847, 1010, 1192, 1394, 1617, 1862, 2130, 2422, 2739, 3082, 3452, 3850, 4277, 4734, 5222, 5742, 6295, 6882, 7504, 8162, 8857, 9590, 10362, 11174, 12027, 12922, 13860, 14842, 15869, 16942, 18062

Offset: 0

Author

N. J. A. Sloane, May 28 2005

Keywords

• nonn
• easy

Links

• W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A007290, A059317.

Programs

Mathematica

Join[{0,0}, LinearRecurrence[{4, -6, 4, -1}, {0, 2, 9, 22}, 45]] (* Georg Fischer, Dec 10 2019 *)

PARI

a(n)=if(n>2,(n-2)*(n^2 + 8*n - 21)/6,0) \\ Charles R Greathouse IV, Oct 18 2022

Formula

For n>1, a(n) = (1/6)*(n-2)*(n^2 + 8n - 21).

From R. J. Mathar, Feb 06 2010: (Start)

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

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

E.g.f.: exp(x)*(42 - 30*x + 9*x^2 + x^3)/6 - 7 - 2*x. - Stefano Spezia, Aug 06 2025