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

Author

R. H. Hardin, May 29 2012

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 6 of A212868.

Programs

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

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).