Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-8) - 2*a(n-9) + a(n-10) - 2*a(n-11) + a(n-12).
Empirical for n mod 12 = 0: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + 1
Empirical for n mod 12 = 1: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n - (17/18)
Empirical for n mod 12 = 2: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (1009/9)
Empirical for n mod 12 = 3: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (167/2)
Empirical for n mod 12 = 4: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (329/9)
Empirical for n mod 12 = 5: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (1343/18)
Empirical for n mod 12 = 6: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + 1
Empirical for n mod 12 = 7: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (2143/18)
Empirical for n mod 12 = 8: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (1009/9)
Empirical for n mod 12 = 9: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n - (73/2)
Empirical for n mod 12 = 10: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + 91*n + (329/9)
Empirical for n mod 12 = 11: a(n) = (15/2)*n^4 + (280/9)*n^3 - (320/3)*n^2 + (193/3)*n + (3503/18).
Empirical g.f.: x*(22 + 139*x + 500*x^2 + 1056*x^3 + 1640*x^4 + 2001*x^5 + 1542*x^6 + 383*x^7 - 102*x^8 - 700*x^9 - 2*x^10 + x^11) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, Nov 08 2018
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