A106173 7th diagonal of triangle in A059317.

0, 0, 0, 0, 1, 13, 72, 255, 691, 1574, 3177, 5867, 10121, 16543, 25882, 39051, 57147, 81472, 113555, 155175, 208385, 275537, 359308, 462727, 589203, 742554, 927037, 1147379, 1408809, 1717091, 2078558, 2500147, 2989435, 3554676, 4204839, 4949647, 5799617

Offset: 0

Author

N. J. A. Sloane, May 28 2005

Keywords

• nonn

Comments

a(n) is a 6th degree polynomial in n.

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 (7, -21, 35, -35, 21, -7, 1).

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,0,0,1,13,72,255,691,1574,3177},40] (* Harvey P. Dale, Jun 26 2022 *)

Formula

From Chai Wah Wu, Feb 28 2018: (Start)

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 10.

G.f.: x^4*(x^6 - 6*x^5 + 2*x^4 + 11*x^3 - 2*x^2 - 6*x - 1)/(x - 1)^7. (End)