A241618 Number of length n+2 0..12 arrays with no consecutive three elements summing to more than 12.

455, 3185, 22295, 145873, 980031, 6645821, 44678543, 300535053, 2025793471, 13644835113, 91879275469, 618858084619, 4168290681519, 28073432645895, 189079333842687, 1273493381875147, 8577194140275861, 57768891197339641

Offset: 1

Author

R. H. Hardin, Apr 26 2014

Keywords

• nonn

Comments

Column 12 of A241619

Examples

			Some solutions for n=5
..0....3....0....0....0....3....3....3....0....3....3....3....0....3....0....0
..6....3....0....0....0....3....0....0....3....3....0....6....0....3....3....9
..0....0....0....2...11....3....8....2....6....4....5....1....7....1....0....0
..3....0....6....8....0....0....2....0....1....4....0....0....5....1....0....1
..2....1....1....0....1....3....2....4....4....1....7....1....0....0....7....7
..2....2....4....1....1....7....3....3....4....1....0....1....5....7....0....1
..4....4....0....9....7....0....0....0....0...10....1....5....0....5....3....0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• R. H. Hardin, Empirical recurrence of order 91
• Robert Israel, Maple-assisted proof of empirical formula

Programs

Maple

r:= [seq(seq([i,j],j=0..12-i),i=0..12)]:
T:= Matrix(91,91,proc(i,j) if r[i][1]=r[j][2] and r[i][1]+r[i][2]+r[j][1]<=12 then 1 else 0 fi end proc):
U[0]:= Vector(91,1):
for n from 1 to 40 do U[n]:= T . U[n-1] od:
seq(U[0]^%T . U[j], j=1..40); # Robert Israel, Sep 03 2019

Formula

Empirical recurrence of order 91 (see link above).

Empirical formula verified (see link). - Robert Israel, Sep 03 2019