The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A265624 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A265624

Array T(n,k): The number of words of length n in an alphabet of size k which do not contain 4 consecutive letters.
(history; published version)

#13 by Peter Luschny at Sat Dec 12 08:06:46 EST 2015

STATUS

reviewed

approved

#12 by R. J. Mathar at Fri Dec 11 04:02:12 EST 2015

STATUS

proposed

reviewed

Discussion

Fri Dec 11

04:21

Alois P. Heinz: Sure.  But the number of words of length 0 in any alphabet is 1 not 0.

#11 by R. J. Mathar at Fri Dec 11 04:02:08 EST 2015

STATUS

editing

proposed

#10 by R. J. Mathar at Fri Dec 11 04:02:02 EST 2015

DATA

1, 1, 2, 1, 4, 3, 0, 8, 9, 4, 0, 14, 27, 16, 5, 0, 26, 78, 64, 25, 6, 0, 48, 228, 252, 125, 36, 7, 0, 88, 666, 996, 620, 216, 49, 8, 0, 162, 1944, 3936, 3080, 1290, 343, 64, 9, 0, 298, 5676, 15552, 15300, 7710, 2394, 512, 81, 10, 0, 548, 16572, 61452, 76000, 46080, 16716, 4088, 729, 100, 11, 0, 1008, 48384, 242820

STATUS

proposed

editing

#9 by R. J. Mathar at Fri Dec 11 04:01:09 EST 2015

STATUS

editing

proposed

#8 by R. J. Mathar at Fri Dec 11 04:00:16 EST 2015

FORMULA

G.f. of row k: (k*x+*(1)*(+x+x^2+1)/(1+(1-k)*x*(x^2+x+1)).

MAPLE

(k*x+*(1)*(+x+x^2+1)/(1+(1-k)*x*(x^2+x+1)) ;

Discussion

Fri Dec 11

04:01

R. J. Mathar: I have undone these changes. There is no reason to enter that pseudo-debate about counting voids here, and my version was entirely correct.

#7 by Alois P. Heinz at Thu Dec 10 16:39:27 EST 2015

FORMULA

G.f . of row k: k*(x*(+1+x+)*(x^2+1)/(1-+(k-1)*x-(k-1)*x*(x^2-(k-+x+1)*x^3).

MAPLE

k*(x*(+1+x+)*(x^2+1)/(1-+(k-1)*x-(k-1)*x*(x^2-(k-+x+1)*x^3) ;

STATUS

proposed

editing

Discussion

Thu Dec 10

16:44

Alois P. Heinz: I replaced the g.f.  Terms in the range plotted here (n>=1 and k>=1) do not change.  But I would suggest to expand the table to range n>=0 and k>=0.

#6 by Michel Marcus at Thu Dec 10 13:40:20 EST 2015

STATUS

editing

proposed

Discussion

Thu Dec 10

15:17

Alois P. Heinz: Should have started with n=0: A265624(0,k)=1 (n=0 counts the empty word); see also A188714 where it is correct.  Program here gives 0 for n=0.

#5 by Michel Marcus at Thu Dec 10 13:40:10 EST 2015

FORMULA

T(2,k) = k^2.

T(3,k) = k^3.

T(4,k) = k*(k+1)*(k^2+3*k+3).

T(5,k) = k*(k+1)*(k^3+4*k^2+6*k+2).

T(6,k) = k*(k+1)^2*(k^3+4*k^2+6*k+1).

EXAMPLE

1 2 3 4 5 6 7 8

STATUS

proposed

editing

#4 by R. J. Mathar at Thu Dec 10 13:09:57 EST 2015

STATUS

editing

proposed