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

0,4

Links

Table of n, a(n) for n=0..46.

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).

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A007290, A059317.

Sequence in context: A056105 A323891 A212069 * A086718 A023625 A166754

Adjacent sequences: A106055 A106056 A106057 * A106059 A106060 A106061

Keyword

nonn,easy

Author

N. J. A. Sloane, May 28 2005

Status

approved