A200250 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 8.

8, 36, 164, 750, 3434, 15724, 71970, 329455, 1508139, 6903702, 31602661, 144665637, 662227235, 3031438038, 13876832881, 63523149100, 290786125630, 1331114279973, 6093362338144, 27893220846536, 127685131134366, 584496598744029

Offset

1,1

Comments

Column 7 of A200251.

Links

R. H. Hardin, Table of n, a(n) for n = 1..134

Formula

Empirical: a(n) = a(n-1) +9*a(n-2) +24*a(n-3) +36*a(n-4) +35*a(n-5) +21*a(n-6) +7*a(n-7) +a(n-8).

Empirical g.f.: x*(2 + x)*(2 + 2*x + x^2)*(2 + 4*x + 6*x^2 + 4*x^3 + x^4) / (1 - x - 9*x^2 - 24*x^3 - 36*x^4 - 35*x^5 - 21*x^6 - 7*x^7 - x^8). - Colin Barker, May 20 2018

Example

Some solutions for n=6:
..3....1....6....3....2....3....2....1....0....6....3....3....0....7....2....1
..6....3....7....7....6....5....6....4....3....6....7....5....2....7....6....4
..7....6....7....7....4....2....3....5....6....7....6....1....7....7....3....5
..5....2....4....1....5....2....6....7....3....6....6....1....5....6....6....6
..5....5....1....3....6....5....1....3....7....2....6....3....6....7....5....2
..7....5....5....6....7....3....5....4....5....7....5....6....7....7....7....7

Crossrefs

Cf. A200251.

Sequence in context: A228702 A200667 A200468 * A207099 A055064 A014347

Adjacent sequences: A200247 A200248 A200249 * A200251 A200252 A200253

Keyword

nonn

Author

R. H. Hardin, Nov 15 2011

Status

approved