OFFSET
1,1
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 2*a(n-5) + 2*a(n-6) - 4*a(n-7) + 5*a(n-8) - 6*a(n-9) + 4*a(n-10) - a(n-11).
Also a polynomial of degree 5 plus a constant pseudonomial with period 12:
Empirical for n mod 12 = 0: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n
Empirical for n mod 12 = 1: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (65/12)
Empirical for n mod 12 = 2: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (20/3)
Empirical for n mod 12 = 3: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (35/4)
Empirical for n mod 12 = 4: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (40/3)
Empirical for n mod 12 = 5: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (145/12)
Empirical for n mod 12 = 6: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n
Empirical for n mod 12 = 7: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (55/12)
Empirical for n mod 12 = 8: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (20/3)
Empirical for n mod 12 = 9: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (75/4)
Empirical for n mod 12 = 10: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n - (40/3)
Empirical for n mod 12 = 11: a(n) = n^5 + (15/4)*n^4 + (25/3)*n^3 + (15/2)*n^2 + 4*n + (25/12).
Empirical g.f.: 10*x*(3 + 7*x + 28*x^2 + 19*x^3 + 50*x^4 + 5*x^5 + 32*x^6 - 3*x^7 + 3*x^8) / ((1 - x)^6*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 09 2018
EXAMPLE
Some solutions for n=6:
2 4 0 0 6 6 0 6 4 0 1 4 2 4 2 5
3 3 2 6 5 0 1 3 6 0 3 6 1 3 4 1
4 6 0 6 4 0 5 6 0 6 4 0 5 3 6 2
3 0 3 1 2 4 5 0 0 0 4 5 6 1 0 5
5 0 2 2 0 6 6 5 3 1 5 6 5 2 2 1
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 29 2014
STATUS
approved