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A241618 Number of length n+2 0..12 arrays with no consecutive three elements summing to more than 12 2
455, 3185, 22295, 145873, 980031, 6645821, 44678543, 300535053, 2025793471, 13644835113, 91879275469, 618858084619, 4168290681519, 28073432645895, 189079333842687, 1273493381875147, 8577194140275861, 57768891197339641 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 10:22 EST 2020. Contains 331193 sequences. (Running on oeis4.)