A011923 [ n(n-1)(n-2)(n-3)/13 ].
0, 0, 0, 0, 1, 9, 27, 64, 129, 232, 387, 609, 913, 1320, 1848, 2520, 3360, 4393, 5649, 7155, 8944, 11049, 13504, 16347, 19617, 23353, 27600, 32400, 37800, 43848, 50593, 58089, 66387, 75544, 85617, 96664
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 6, -4, 1).
Programs
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PARI
a(n)=n*(n-1)*(n-2)*(n-3)\13 \\ Charles R Greathouse IV, Oct 18 2022
Formula
From Chai Wah Wu, Aug 02 2020: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-13) - 4*a(n-14) + 6*a(n-15) - 4*a(n-16) + a(n-17) for n > 16.
G.f.: x^4*(-x^12 - 5*x^11 + 3*x^10 - 6*x^9 - x^7 - 4*x^6 - x^5 - 6*x^3 + 3*x^2 - 5*x - 1)/(x^17 - 4*x^16 + 6*x^15 - 4*x^14 + x^13 - x^4 + 4*x^3 - 6*x^2 + 4*x - 1). (End)