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A183901 Number of nondecreasing arrangements of n+3 numbers in 0..6 with each number being the sum mod 7 of three others. 1
1, 1, 136, 664, 1720, 3491, 6263, 10400, 16357, 24694, 36091, 51364, 71482, 97585, 131003, 173276, 226175, 291724, 372223, 470272, 588796, 731071, 900751, 1101896, 1339001, 1617026, 1941427, 2318188, 2753854, 3255565, 3831091, 4488868, 5238035 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 6 of A183904.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..37

FORMULA

Empirical: a(n) = (1/720)*n^6 + (13/240)*n^5 + (125/144)*n^4 + (117/16)*n^3 + (12287/360)*n^2 - (4421/30)*n - 44 for n>3.

Conjectures from Colin Barker, Apr 05 2018: (Start)

G.f.: x*(1 - 6*x + 150*x^2 - 302*x^3 - 72*x^4 + 649*x^5 - 548*x^6 + 60*x^7 + 102*x^8 - 33*x^9) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.

(End)

EXAMPLE

Some solutions for n=3:

..0....0....3....0....0....0....0....0....0....0....0....1....0....0....2....1

..1....0....3....1....0....0....0....3....2....1....1....1....3....0....4....2

..1....1....3....1....1....3....1....4....3....2....4....2....3....1....4....3

..2....1....4....4....2....3....1....5....4....3....5....3....4....2....5....3

..4....2....4....4....2....5....3....6....4....4....5....4....5....4....5....5

..4....4....4....6....4....6....3....6....6....4....6....5....5....4....6....6

CROSSREFS

Cf. A183904.

Sequence in context: A235198 A235191 A076331 * A270341 A234169 A234162

Adjacent sequences:  A183898 A183899 A183900 * A183902 A183903 A183904

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 07 2011

STATUS

approved

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)