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

1,1

Comments

Column 12 of A241619

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

Formula

Empirical recurrence of order 91 (see link above).

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

Example

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

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

Crossrefs

Sequence in context: A043475 A324633 A260735 * A251337 A282232 A061544

Adjacent sequences: A241615 A241616 A241617 * A241619 A241620 A241621

Keyword

nonn

Author

R. H. Hardin, Apr 26 2014

Status

approved