A106173 - OEIS

%I #19 Jan 05 2025 19:51:38

%S 0,0,0,0,1,13,72,255,691,1574,3177,5867,10121,16543,25882,39051,57147,

%T 81472,113555,155175,208385,275537,359308,462727,589203,742554,927037,

%U 1147379,1408809,1717091,2078558,2500147,2989435,3554676,4204839,4949647,5799617

%N 7th diagonal of triangle in A059317.

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

%H W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/35-4/klostermeyer.pdf">A Pascal rhombus</a>, Fibonacci Quarterly, 35 (1997), 318-328.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).

%F From _Chai Wah Wu_, Feb 28 2018: (Start)

%F 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.

%F 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)

%t 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 *)

%K nonn

%O 0,6

%A _N. J. A. Sloane_, May 28 2005