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

0,6

Comments

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

Links

Table of n, a(n) for n=0..36.

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).

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)

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 *)

Crossrefs

Sequence in context: A104132 A096913 A026916 * A094943 A189605 A000470

Adjacent sequences: A106170 A106171 A106172 * A106174 A106175 A106176

Keyword

nonn

Author

N. J. A. Sloane, May 28 2005

Status

approved