A183911 Number of nondecreasing arrangements of n+2 numbers in 0..8 with each number being the sum mod 9 of two others.

1, 4, 31, 231, 1093, 3631, 9576, 21660, 43980, 82453, 145376, 244106, 393876, 614764, 932833, 1381461, 2002881, 2849952, 3988183, 5498033, 7477511, 10045101, 13343038, 17540962, 22839978, 29477151, 37730466, 47924284, 60435326, 75699218

Offset

1,2

Comments

Column 8 of A183912.

Links

R. H. Hardin, Table of n, a(n) for n = 1..52

Formula

Empirical: a(n) = (1/40320)*n^8 + (13/10080)*n^7 + (83/2880)*n^6 + (13/36)*n^5 + (15967/5760)*n^4 - (45839/1440)*n^3 + (59583/1120)*n^2 + (20743/168)*n - 297 for n>3.

Conjectures from Colin Barker, Apr 06 2018: (Start)

G.f.: x*(1 - 5*x + 31*x^2 + 12*x^3 - 80*x^4 - 116*x^5 + 327*x^6 - 120*x^7 - 147*x^8 + 120*x^9 - 20*x^10 - 2*x^11) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.

(End)

Example

All solutions for n=2:
..0....0....3....0
..3....0....3....3
..3....0....6....6
..6....0....6....6

Crossrefs

Cf. A183912.

Sequence in context: A124033 A014537 A136284 * A039765 A001091 A309184

Adjacent sequences: A183908 A183909 A183910 * A183912 A183913 A183914

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved