A200252 Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).

5, 12, 26, 45, 75, 112, 164, 225, 305, 396, 510, 637, 791, 960, 1160, 1377, 1629, 1900, 2210, 2541, 2915, 3312, 3756, 4225, 4745, 5292, 5894, 6525, 7215, 7936, 8720, 9537, 10421, 11340, 12330, 13357, 14459, 15600, 16820, 18081, 19425, 20812, 22286, 23805

Offset: 1

Author

R. H. Hardin, Nov 15 2011

Keywords

• nonn
• easy

Comments

Row 3 of A200251.

a(n) = A199771(n+1). - Reinhard Zumkeller, Nov 23 2011

Examples

			Some solutions for n=6:
  2  0  0  3  3  1  4  0  1  3  0  3  0  2  1  3
  6  5  3  6  3  1  5  2  4  6  6  5  0  5  2  4
  2  6  6  2  6  4  4  2  6  5  6  5  6  5  4  0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

From Colin Barker, Feb 19 2018: (Start)

G.f.: x*(5 + 2*x - 3*x^2 + x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).

a(n) = (n^3 + 5*n^2 + 8*n + 4) / 4 for n even.

a(n) = (n^3 + 5*n^2 + 9*n + 5) / 4 for n odd.

(End)