login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188843 T(n,k)=Number of nXk binary arrays without the pattern 0 1 diagonally or vertically 6
2, 4, 3, 8, 8, 4, 16, 21, 13, 5, 32, 55, 40, 19, 6, 64, 144, 121, 66, 26, 7, 128, 377, 364, 221, 100, 34, 8, 256, 987, 1093, 728, 364, 143, 43, 9, 512, 2584, 3280, 2380, 1288, 560, 196, 53, 10, 1024, 6765, 9841, 7753, 4488, 2108, 820, 260, 64, 11, 2048, 17711, 29524 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..2..4...8...16...32....64....128....256.....512.....1024.....2048......4096

..3..8..21...55..144...377....987...2584....6765....17711....46368....121393

..4.13..40..121..364..1093...3280...9841...29524....88573...265720....797161

..5.19..66..221..728..2380...7753..25213...81927...266110...864201...2806272

..6.26.100..364.1288..4488..15504..53296..182688...625184..2137408...7303360

..7.34.143..560.2108..7752..28101.100947..360526..1282735..4552624..16131656

..8.43.196..820.3264.12597..47652.177859..657800..2417416..8844448..32256553

..9.53.260.1156.4845.19551..76912.297275.1134705..4292145.16128061..60304951

.10.64.336.1581.6954.29260.119416.476905.1874730..7283640.28048800.107286661

.11.76.425.2109.9709.42504.179630.740025.2991495.11920740.46981740.183579396

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1741

FORMULA

Row recurrence

Empirical: T(n,k) = sum(binomial(n+2-i,i)*T(n,k-i)*(-1)^(i-1) , i=1..floor((n+2)/2))

eg.,

Empirical: T(1,k)=2*T(1,k-1)

Empirical: T(2,k)=3*T(2,k-1)-T(2,k-2)

Empirical: T(3,k)=4*T(3,k-1)-3*T(3,k-2)

Empirical: T(4,k)=5*T(4,k-1)-6*T(4,k-2)+T(4,k-3)

Empirical: T(5,k)=6*T(5,k-1)-10*T(5,k-2)+4*T(5,k-3)

Empirical: T(6,k)=7*T(6,k-1)-15*T(6,k-2)+10*T(6,k-3)-T(6,k-4)

Empirical: T(7,k)=8*T(7,k-1)-21*T(7,k-2)+20*T(7,k-3)-5*T(7,k-4)

Empirical: T(8,k)=9*T(8,k-1)-28*T(8,k-2)+35*T(8,k-3)-15*T(8,k-4)+T(8,k-5)

Columns are polynomials for n>k-3

Empirical: T(n,1) = n + 1

Empirical: T(n,2) = (1/2)*n^2 + (5/2)*n + 1

Empirical: T(n,3) = (1/6)*n^3 + 2*n^2 + (35/6)*n

Empirical: T(n,4) = (1/24)*n^4 + (11/12)*n^3 + (155/24)*n^2 + (163/12)*n - 6 for n>1

Empirical: T(n,5) = (1/120)*n^5 + (7/24)*n^4 + (89/24)*n^3 + (473/24)*n^2 + (1877/60)*n - 33 for n>2

Empirical: T(n,6) = (1/720)*n^6 + (17/240)*n^5 + (203/144)*n^4 + (647/48)*n^3 + (2659/45)*n^2 + (1379/20)*n - 143 for n>3

Empirical: T(n,7) = (1/5040)*n^7 + (1/72)*n^6 + (143/360)*n^5 + (53/9)*n^4 + (33667/720)*n^3 + (12679/72)*n^2 + (9439/70)*n - 572 for n>4

Empirical: T(n,8) = (1/40320)*n^8 + (23/10080)*n^7 + (17/192)*n^6 + (269/144)*n^5 + (43949/1920)*n^4 + (228401/1440)*n^3 + (1054411/2016)*n^2 + (9941/56)*n - 2210 for n>5

EXAMPLE

Some solutions for 5X3

..0..0..1....1..1..0....1..1..1....0..1..0....1..1..0....1..1..0....1..1..1

..0..0..0....1..0..0....1..1..0....0..0..0....1..1..0....1..1..0....1..1..1

..0..0..0....0..0..0....1..1..0....0..0..0....1..0..0....1..1..0....0..1..1

..0..0..0....0..0..0....1..1..0....0..0..0....1..0..0....1..0..0....0..0..0

..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

CROSSREFS

Diagonal is A143388

Column 2 is A034856(n+1)

Column 3 is A137742(n+1)

Row 2 is A001906(n+1)

Row 3 is A003462(n+1)

Row 4 is A005021

Row 5 is A005022

Row 6 is A005023

Row 7 is A005024

Row 8 is A005025

Sequence in context: A237739 A111699 A067179 * A209406 A188706 A048767

Adjacent sequences:  A188840 A188841 A188842 * A188844 A188845 A188846

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 12 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 5 03:30 EST 2016. Contains 278755 sequences.