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%I #13 Oct 21 2022 21:22:47
%S 0,0,0,1,8,29,72,146,261,428,659,967,1366,1871,2498,3264,4187,5286,
%T 6581,8093,9844,11857,14156,16766,19713,23024,26727,30851,35426,40483,
%U 46054,52172,58871,66186,74153,82809,92192,102341,113296,125098,137789,151412
%N 5th diagonal of triangle in A059317.
%H W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, <a href="http://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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F For n>2, a(n) = (1/24) [n^4 + 14n^3 - 97n^2 + 154n - 24 ].
%F From _Chai Wah Wu_, Mar 11 2021: (Start)
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 7.
%F G.f.: x^3*(-x^4 + 3*x^3 + x^2 - 3*x - 1)/(x - 1)^5. (End)
%o (PARI) a(n)=if(n>2,n^4 + 14*n^3 - 97*n^2 + 154*n - 24,0)/24 \\ _Charles R Greathouse IV_, Oct 21 2022
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_, May 28 2005
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