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

%I A241618 #11 Jun 02 2025 10:11:08
%S A241618 455,3185,22295,145873,980031,6645821,44678543,300535053,2025793471,
%T A241618 13644835113,91879275469,618858084619,4168290681519,28073432645895,
%U A241618 189079333842687,1273493381875147,8577194140275861,57768891197339641
%N A241618 Number of length n+2 0..12 arrays with no consecutive three elements summing to more than 12.
%C A241618 Column 12 of A241619
%H A241618 R. H. Hardin, <a href="/A241618/b241618.txt">Table of n, a(n) for n = 1..210</a>
%H A241618 R. H. Hardin, <a href="/A241618/a241618.txt">Empirical recurrence of order 91</a>
%H A241618 Robert Israel, <a href="/A241618/a241618.pdf">Maple-assisted proof of empirical formula</a>
%F A241618 Empirical recurrence of order 91 (see link above).
%F A241618 Empirical formula verified (see link). - _Robert Israel_, Sep 03 2019
%e A241618 Some solutions for n=5
%e A241618 ..0....3....0....0....0....3....3....3....0....3....3....3....0....3....0....0
%e A241618 ..6....3....0....0....0....3....0....0....3....3....0....6....0....3....3....9
%e A241618 ..0....0....0....2...11....3....8....2....6....4....5....1....7....1....0....0
%e A241618 ..3....0....6....8....0....0....2....0....1....4....0....0....5....1....0....1
%e A241618 ..2....1....1....0....1....3....2....4....4....1....7....1....0....0....7....7
%e A241618 ..2....2....4....1....1....7....3....3....4....1....0....1....5....7....0....1
%e A241618 ..4....4....0....9....7....0....0....0....0...10....1....5....0....5....3....0
%p A241618 r:= [seq(seq([i,j],j=0..12-i),i=0..12)]:
%p A241618 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 A241618 U[0]:= Vector(91,1):
%p A241618 for n from 1 to 40 do U[n]:= T . U[n-1] od:
%p A241618 seq(U[0]^%T . U[j], j=1..40); # _Robert Israel_, Sep 03 2019
%K A241618 nonn
%O A241618 1,1
%A A241618 _R. H. Hardin_, Apr 26 2014