A212866 Number of nondecreasing sequences of n 1..6 integers with no element dividing the sequence sum.

0, 7, 16, 29, 52, 82, 122, 182, 259, 363, 492, 648, 816, 1018, 1268, 1586, 1973, 2419, 2904, 3452, 4063, 4762, 5543, 6421, 7393, 8487, 9700, 11052, 12543, 14183, 15960, 17915, 20023, 22303, 24760, 27422, 30279, 33373, 36697, 40284, 44131, 48250, 52614

Offset

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +2*a(n-4) +a(n-5) +a(n-6) -4*a(n-7) +4*a(n-9) -a(n-10) -a(n-11) -a(n-12) -a(n-13) +4*a(n-14) -4*a(n-16) +a(n-17) +a(n-18) +2*a(n-19) -a(n-20) -5*a(n-21) +5*a(n-22) +a(n-23) -2*a(n-24) -a(n-25) -a(n-26) +4*a(n-27) -4*a(n-29) +a(n-30) +a(n-31) +a(n-32) +a(n-33) -4*a(n-34) +4*a(n-36) -a(n-37) -a(n-38) -2*a(n-39) +2*a(n-40) +2*a(n-41) -3*a(n-42) +a(n-43).

Example

Some solutions for n=8:
..2....3....2....2....2....2....3....3....2....2....2....2....4....5....3....2
..2....3....2....2....3....5....3....4....2....3....2....2....4....5....3....3
..2....3....3....2....3....6....4....4....3....4....2....3....4....5....3....3
..3....3....3....2....3....6....4....4....3....4....2....3....5....5....3....3
..3....3....4....2....6....6....4....5....4....4....2....4....6....6....3....3
..3....3....5....2....6....6....4....6....4....4....2....5....6....6....5....3
..4....3....6....4....6....6....4....6....5....5....2....5....6....6....6....3
..4....4....6....5....6....6....5....6....6....5....5....5....6....6....6....3

Maple

S6:= combinat:-powerset({$2..6}):
f:= proc(n) local s, t, G, S, i, j, T;
  t:= 0:
  for S in S6 do
    G:= coeff(mul(add(x^i*y^(i*j), i=0..n), j=S), x, n);
    T:= select(s -> S = select(k -> s mod k <> 0, {$2..6}), [$2*n..6*n]);
    t:= t + add(coeff(G, y, s), s= T);
  od;
  t
end proc:
map(f, [$1..50]); # Robert Israel, Nov 23 2023

Crossrefs

Column 6 of A212868.

Sequence in context: A024627 A211784 A180724 * A234717 A364352 A140511

Adjacent sequences: A212863 A212864 A212865 * A212867 A212868 A212869

Keyword

nonn

Author

R. H. Hardin, May 29 2012

Status

approved