A241618 - OEIS

%I #9 Sep 04 2019 02:55:11

%S 455,3185,22295,145873,980031,6645821,44678543,300535053,2025793471,

%T 13644835113,91879275469,618858084619,4168290681519,28073432645895,

%U 189079333842687,1273493381875147,8577194140275861,57768891197339641

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

%C Column 12 of A241619

%H R. H. Hardin, <a href="/A241618/b241618.txt">Table of n, a(n) for n = 1..210</a>

%H R. H. Hardin, <a href="/A241618/a241618.txt">Empirical recurrence of order 91</a>

%H Robert Israel, <a href="/A241618/a241618.pdf">Maple-assisted proof of empirical formula</a>

%F Empirical recurrence of order 91 (see link above).

%F Empirical formula verified (see link). - _Robert Israel_, Sep 03 2019

%e Some solutions for n=5

%e ..0....3....0....0....0....3....3....3....0....3....3....3....0....3....0....0

%e ..6....3....0....0....0....3....0....0....3....3....0....6....0....3....3....9

%e ..0....0....0....2...11....3....8....2....6....4....5....1....7....1....0....0

%e ..3....0....6....8....0....0....2....0....1....4....0....0....5....1....0....1

%e ..2....1....1....0....1....3....2....4....4....1....7....1....0....0....7....7

%e ..2....2....4....1....1....7....3....3....4....1....0....1....5....7....0....1

%e ..4....4....0....9....7....0....0....0....0...10....1....5....0....5....3....0

%p r:= [seq(seq([i,j],j=0..12-i),i=0..12)]:

%p 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):

%p U[0]:= Vector(91,1):

%p for n from 1 to 40 do U[n]:= T . U[n-1] od:

%p seq(U[0]^%T . U[j], j=1..40); # _Robert Israel_, Sep 03 2019

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 26 2014