A106113 5th diagonal of triangle in A059317.
0, 0, 0, 1, 8, 29, 72, 146, 261, 428, 659, 967, 1366, 1871, 2498, 3264, 4187, 5286, 6581, 8093, 9844, 11857, 14156, 16766, 19713, 23024, 26727, 30851, 35426, 40483, 46054, 52172, 58871, 66186, 74153, 82809, 92192, 102341, 113296, 125098, 137789, 151412
Offset: 0
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 (5,-10,10,-5,1).
Programs
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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
Formula
For n>2, a(n) = (1/24) [n^4 + 14n^3 - 97n^2 + 154n - 24 ].
From Chai Wah Wu, Mar 11 2021: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 7.
G.f.: x^3*(-x^4 + 3*x^3 + x^2 - 3*x - 1)/(x - 1)^5. (End)