A063443 -id:A063443 - cp's OEIS frontend

A247413 Decimal expansion of the entropy constant related to A063443.

1, 3, 4, 2, 6, 4, 3, 9, 5, 1, 1, 2, 4

Offset: 1

Vaclav Kotesovec, Sep 16 2014

			1.342643951124...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 343.
B. D. McKay, On Calkin and Wilf's limit theorem for grid graphs, unpublished note, 1996.

N. J. Calkin, K. James, and S. Purvis, Counting Kings, 2006, p.9.
N. J. Calkin and H. S. Wilf, The number of independent sets in a grid graph, preprint, 1995.
N. J. Calkin and H. S. Wilf, The number of independent sets in a grid graph, SIAM J. Discrete Math, 11 (1998) 54-60.
Steven R. Finch, Several Constants Arising in Statistical Mechanics, arXiv:math/9810155 [math.CO], 1999, p.8.
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p.68-69.
D. E. Knuth, Nonattacking kings on a chessboard, 1994.
M. Larsen, The Problem of Kings, The Electronic Journal of Combinatorics 2, 1995.
Kai Liang, Independent Set Enumeration in King Graphs by Tensor Network Contractions, arXiv:2505.12776 [math.CO], 2025. See p. 6.
Eric Weisstein's World of Mathematics, Hard Hexagon Entropy Constant
Eric Weisstein's World of Mathematics, Hard Square Entropy Constant
H. S. Wilf, The problem of the kings, Elec. J. Combin. 2, 1995.

Cf. A063443, A212269.

Cf. A085850, A085851.

Equals limit n->infinity (A063443(n))^(1/n^2).

Equals limit n->infinity (A212269(n))^(1/n^2).

A045846 Number of distinct ways to cut an n X n square into squares with integer sides.

Original entry on oeis.org

1, 1, 2, 6, 40, 472, 10668, 450924, 35863972, 5353011036, 1500957422222, 790347882174804, 781621363452405930, 1451740730942350766748, 5064070747064013556294032, 33176273260130056822126522884, 408199838581532754602910469192704

Offset: 0

Erich Friedman

			For n=3 the 6 dissections are: the full 3 X 3 square; 9 1 X 1 squares; one 2 X 2 square and five 1 X 1 squares (in 4 ways).

Andrew Gozzard and Max Ward, Table of n, a(n) for n = 0..25 (terms 0..20 from Steve Butler).
Steve Butler, Jason Ekstrand, Steven Osborne, Counting Tilings by Taking Walks in a Graph, A Project-Based Guide to Undergraduate Research in Mathematics, Birkhäuser, Cham (2020), see page 169.
N. J. A. Sloane, Illustration of the first five terms of A045846 and A224239, page 1 of 4 (Each dissection from A224239 is labeled with the number of its images under the symmetry group of the square. The sum of these numbers is A045846(n).)
N. J. A. Sloane, Illustration of the first five terms of A045846 and A224239, page 2 of 4 (The largest squares are drawn in red. The next-largest squares, unless of size 1, are drawn in blue.)
N. J. A. Sloane, Illustration of the first five terms of A045846 and A224239, page 3 of 4 (The largest squares are drawn in red. The next-largest squares, unless of size 1, are drawn in blue.)
N. J. A. Sloane, Illustration of the first five terms of A045846 and A224239, page 4 of 4 (The largest squares are drawn in red. The next-largest squares, unless of size 1, are drawn in blue.)
Ed Wynn, Exhaustive generation of Mrs Perkins's quilt square dissections for low orders, arXiv:1308.5420 [math.CO], 2013-2014.

Diagonal of A219924. - Alois P. Heinz, Dec 01 2012
See A224239 for the number of inequivalent ways.
Cf. A034295, A063443, A211348, A226554.

b:= proc(n, l) option remember; local i, k, s, t;
      if max(l[])>n then 0 elif n=0 or l=[] then 1
    elif min(l[])>0 then t:=min(l[]); b(n-t, map(h->h-t, l))
    else for k do if l[k]=0 then break fi od; s:=0;
         for i from k to nops(l) while l[i]=0 do s:=s+
           b(n, [l[j]$j=1..k-1, 1+i-k$j=k..i, l[j]$j=i+1..nops(l)])
         od; s
      fi
    end:
a:= n-> b(n, [0$n]):
seq(a(n), n=0..11);  # Alois P. Heinz, Apr 15 2013

$RecursionLimit = 1000; b[n_, l_List] := b[n, l] = Module[{i, k, s, t}, Which[ Max[l]>n, 0, n == 0 || l == {}, 1, Min[l]>0, t = Min[l]; b[n-t, l-t], True, For[k = 1, True, k++, If[l[[k]] == 0, Break[]]]; s=0; For[i=k, i <= Length[l] && l[[i]] == 0, i++, s = s + b[n, Join[l[[1 ;; k-1]], Table[1+i-k, {i-k+1}], l[[i+1 ;; Length[l]]]]]]; s]]; a[n_] := b[n, Array[0&, n]]; Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Feb 25 2015, after Alois P. Heinz *)

It appears lim n->oo a(n)*a(n-3)/(a(n-1)*a(n-2)) = 3.527... - Gerald McGarvey, May 03 2005
It appears that lim n->oo a(n)*a(n-2)/(a(n-1))^2 = 1.8781... - Christopher Hunt Gribble, Jun 21 2013
a(n) = (1/n^2) * Sum_{k=1..n} k^2 * A226936(n,k). - Alois P. Heinz, Jun 22 2013

More terms from Hugo van der Sanden, Nov 06 2000
a(14)-a(15) from Alois P. Heinz, Nov 30 2012
a(16) from Steve Butler, Mar 14 2014

A067966 Number of binary arrangements without adjacent 1's on n X n array connected n-s.

Original entry on oeis.org

1, 2, 9, 125, 4096, 371293, 85766121, 52523350144, 83733937890625, 350356403707485209, 3833759992447475122176, 109879109551310452512114617, 8243206936713178643875538610721, 1619152874321527556575810000000000000

Offset: 0

R. H. Hardin, Feb 02 2002

Central coefficients of triangle A210341.

			Neighbors for n=4:
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o

Vincenzo Librandi, Table of n, a(n) for n = 0..60
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69, 380.

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.

Cf. A100399, A210343, A210341.

[Fibonacci(n+2)^n: n in [0..13]]; // Bruno Berselli, Mar 28 2012

Mathematica
```
Table[Fibonacci[n+2]^n, {n, 0, 100}]
```
Maxima
```
makelist(fib(n+2)^n, n, 0, 14);
```

a(n)=fibonacci(n+2)^n \\ Charles R Greathouse IV, Mar 28 2012

a(n) = F(n+2)^n, where F(n) = A000045(n) is the n-th Fibonacci number.

a(n) ~ phi^2/sqrt(5) phi^n^2. [Charles R Greathouse IV, Mar 28 2012]

Edited by Dean Hickerson, Feb 15 2002

A067961 Number of binary arrangements without adjacent 1's on n X n torus connected n-s.

Original entry on oeis.org

1, 9, 64, 2401, 161051, 34012224, 17249876309, 23811286661761, 84590643846578176, 792594609605189126649, 19381341794579313317802199, 1242425797286480951825250390016, 208396491430277954192889648311785961, 91534759488004239323168528670973468727049

Offset: 1

R. H. Hardin, Feb 02 2002

			Neighbors for n=4:
| | | |
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o
| | | |

Vincenzo Librandi, Table of n, a(n) for n = 1..69
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 409.

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, e-w n-s A027683, e-w ne-sw n-s A066866.
Cf. A156216. - Paul D. Hanna, Sep 13 2010
Cf. A215941.

[Lucas(n)^n: n in [1..15]]; // Vincenzo Librandi, Mar 15 2014

a:= n-> (<<0|1>, <1|1>>^n. <<2, 1>>)[1$2]^n:
seq(a(n), n=1..15);  # Alois P. Heinz, Aug 01 2021

Table[LucasL[n]^n,{n,15}] (* Harvey P. Dale, Mar 13 2014 *)

a(n) = L(n)^n, where L(n) = A000032(n) is the n-th Lucas number.
Logarithmic derivative of A156216. - Paul D. Hanna, Sep 13 2010
Sum_{n>=1} 1/a(n) = A215941. - Amiram Eldar, Nov 17 2020

Edited by Dean Hickerson, Feb 15 2002

A067965 Number of binary arrangements without adjacent 1's on n X n array connected ne-sw and nw-se.

Original entry on oeis.org

2, 9, 119, 2704, 177073, 21836929, 6985036032, 4576976735769, 7263963336910751, 24830487842030082304, 198126078679714777857441, 3494153303407491549112098721, 141264727800378056245286463971328, 12779122891585386852029424628087941481, 2628141044813862018744988536642011269669959

Offset: 1

R. H. Hardin, Feb 02 2002

			Neighbors for n=4 (dots represent spaces):
. o..o..o..o
...\/ \/ \/
.../\ /\ /\
. o..o..o..o
...\/ \/ \/
.../\ /\ /\
. o..o..o..o
...\/ \/ \/
.../\ /\ /\
. o..o..o..o

Liang Kai, Table of n, a(n) for n = 1..27 (first 19 terms from Vaclav Kotesovec)
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69, 417.

Main diagonal of A181212.
Cf. circle A000204, line A000045, arrays: e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.
Cf. A201861, A212271.

Term a(14) from Vaclav Kotesovec, Dec 06 2011
Term a(15) from Vaclav Kotesovec, Jan 03 2012
Term a(16) from Vaclav Kotesovec, May 01 2012
Term a(17)-a(18) from Vaclav Kotesovec, Aug 13 2016

A193580 Triangle read by rows: T(n,k) = number of ways to place k nonattacking kings on an n X n board.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 9, 16, 8, 1, 1, 16, 78, 140, 79, 1, 25, 228, 964, 1987, 1974, 978, 242, 27, 1, 1, 36, 520, 3920, 16834, 42368, 62266, 51504, 21792, 3600, 1, 49, 1020, 11860, 85275, 397014, 1220298, 2484382, 3324193, 2882737, 1601292, 569818, 129657, 18389, 1520, 64, 1

Offset: 0

Andrew Woods, Aug 27 2011

Rows 2n and 2n-1 both contain 1 + n^2 entries. Cf. A008794.
Row n sums to A063443(n+1).
Number of walks of length n-1 on a graph in which each node represents a 11-avoiding n-bit binary sequence B and adjacency of B and B' is determined by B'&(B|(B<<1)|(B>>1))=0 and the total number of nonzero bits in the walk is k.
Row n gives the coefficients of the independence polynomial of the n X n king graph. - Eric W. Weisstein, Jun 20 2017

			The table begins with T(0,0):
  1;
  1,   1;
  1,   4;
  1,   9,  16,   8,   1;
  1,  16,  78, 140,  79;
  ...
T(4,3) = 140 because there are 140 ways to place 3 kings on a 4 X 4 chessboard so that no king threatens any other.

Norman Biggs, Algebraic Graph Theory, Cambridge University Press, New York, NY, second edition, 1993.

Liang Kai, Rows n = 0..26, flattened (Rows n = 0..20 from Andrew Woods, row n = 21 from Alois P. Heinz)
Kai Liang, Independent Set Enumeration in King Graphs by Tensor Network Contractions, arXiv:2505.12776 [math.CO], 2025. See p. 1.
R. J. Mathar, Tiling n x m rectangles with 1 x 1 and s x s squares arXiv:1609.03964 [math.CO], 2016, Section 4.1.
Johan Nilsson, On Counting the Number of Tilings of a Rectangle with Squares of Size 1 and 2, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.2.
Eric Weisstein's World of Mathematics, Independence Polynomial
Eric Weisstein's World of Mathematics, King Graph

Columns 2 to 10: A061995, A061996, A061997, A061998, A172158, A194788, A201369, A201771, A220467.
Diagonal: A201513.
Cf. A179403, etc., for extension to toroidal boards.
Cf. A166540, etc., for extension into three dimensions.
Cf. A098487 for a clipped version.
Row n sums to A063443(n+1).

T(n, 0) = 1;
T(n, 1) = n^2;
T(2n-1, n^2-1) = n^3;
T(2n-1, n^2) = 1.

A067960 Number of binary arrangements without adjacent 1's on n X n torus connected ne-sw nw-se.

Original entry on oeis.org

1, 9, 34, 961, 25531, 2722500, 464483559, 224546142769, 215560806324388, 509113406167679889, 2590618817013278596997, 30737628149641669227004804, 809724336154415150287031740151, 48754690373355654118816600200711441

Offset: 1

R. H. Hardin, Feb 02 2002

If n is odd then A067960(n) = A027683(n).
a(18) = 2184710661251680812138610069332410066909052859790416601664. (a(17) = ?) - Vaclav Kotesovec, Sep 16 2014
a(20) = 61548416926224234005237372092957872593295040887178016957765412173582481. - Vaclav Kotesovec, May 18 2021

			Neighbors for n=4 (dots represent spaces):
.  \ /\ /\ /\ /
.   o..o..o..o
.  / \/ \/ \/ \
.  \ /\ /\ /\ /
.   o..o..o..o
.  / \/ \/ \/ \
.  \ /\ /\ /\ /
.   o..o..o..o
.  / \/ \/ \/ \
.  \ /\ /\ /\ /
.   o..o..o..o
.  / \/ \/ \/ \

Vaclav Kotesovec, Table of n, a(n) for n = 1..16
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 440.

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.

Cf. A212271.

Terms a(12)-a(16) from Vaclav Kotesovec, May 18 2012

A067962 a(n) = F(n+2)*(Product_{i=1..n+1} F(i))^2 where F(i)=A000045(i) is the i-th Fibonacci number.

Original entry on oeis.org

1, 2, 12, 180, 7200, 748800, 204422400, 145957593600, 272940700032000, 1336044726656640000, 17122749216831498240000, 574502481723130428948480000, 50464872497041500009263431680000, 11605406728144633757130311383449600000

Offset: 0

R. H. Hardin, Feb 02 2002

Number of binary arrangements without adjacent 1's on n X n array connected nw-se.

Kitaev and Mansour give a general formula for the number of binary m X n matrices avoiding certain configurations.

			Neighbors for n=4 (dots represent spaces, circles represent grid points):
O..O..O..O
.\..\..\..
..\..\..\.
O..O..O..O
.\..\..\..
..\..\..\.
O..O..O..O
.\..\..\..
..\..\..\.
O..O..O..O

Reinhard Zumkeller, Table of n, a(n) for n = 0..68
Sergey Kitaev and Toufik Mansour, The problem of the pawns, arXiv:math/0305253 [math.CO], 2003; Annals of Combinatorics 8 (2004) 81-91.
Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 69, 421.

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, e-w ne-sw n-s nw-se A067958, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.

Cf. A001654, A003266.

a067962 n = a067962_list !! n
a067962_list = 1 : zipWith (*) a067962_list (drop 2 a001654_list)
-- Reinhard Zumkeller, Sep 24 2015

a:= proc(n) option remember; `if`(n=0, 1, (F->
      F(n+1)*F(n+2)*a(n-1))(combinat[fibonacci]))
    end:
seq(a(n), n=0..14);  # Alois P. Heinz, May 20 2019

Rest[Table[With[{c=Fibonacci[Range[n]]},(Times@@Most[c])^2 Last[c]],{n,15}]] (* Harvey P. Dale, Dec 17 2013 *)

a(n)=fibonacci(n+2)*prod(i=0,n,fibonacci(i+1))^2

a(n) = (F(3) * F(4) * ... * F(n+1))^2 * F(n+2), where F(n) = A000045(n) is the n-th Fibonacci number.
a(n) is asymptotic to C^2*((1+sqrt(5))/2)^((n+2)^2)/(5^(n+3/2)) where C=1.226742010720353244... is the Fibonacci Factorial Constant, see A062073. - Vaclav Kotesovec, Oct 28 2011
a(n) = a(n-1) * A001654(n+1), n > 0. - Reinhard Zumkeller, Sep 24 2015

Edited by Dean Hickerson, Feb 15 2002

Revised by N. J. A. Sloane following comments from Benoit Cloitre, Nov 12 2003

A245013 Number A(n,k) of tilings of a k X n rectangle using 1 X 1 squares and 2 X 2 squares; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 5, 5, 5, 1, 1, 1, 1, 8, 11, 11, 8, 1, 1, 1, 1, 13, 21, 35, 21, 13, 1, 1, 1, 1, 21, 43, 93, 93, 43, 21, 1, 1, 1, 1, 34, 85, 269, 314, 269, 85, 34, 1, 1, 1, 1, 55, 171, 747, 1213, 1213, 747, 171, 55, 1, 1

Offset: 0

Alois P. Heinz, Sep 16 2014

			A(3,3) = 5:
  ._._._.  .___._.  ._.___.  ._._._.  ._._._.
  |_|_|_|  |   |_|  |_|   |  |_|_|_|  |_|_|_|
  |_|_|_|  |___|_|  |_|___|  |_|   |  |   |_|
  |_|_|_|  |_|_|_|  |_|_|_|  |_|___|  |___|_| .
Square array A(n,k) begins:
  1, 1,  1,  1,   1,    1,     1,      1, ...
  1, 1,  1,  1,   1,    1,     1,      1, ...
  1, 1,  2,  3,   5,    8,    13,     21, ...
  1, 1,  3,  5,  11,   21,    43,     85, ...
  1, 1,  5, 11,  35,   93,   269,    747, ...
  1, 1,  8, 21,  93,  314,  1213,   4375, ...
  1, 1, 13, 43, 269, 1213,  6427,  31387, ...
  1, 1, 21, 85, 747, 4375, 31387, 202841, ...

Liang Kai, Antidiagonals n = 0..80, flattened (antidiagonals n = 0..45 from Alois P. Heinz)
Kai Liang, Independent Set Enumeration in King Graphs by Tensor Network Contractions, arXiv:2505.12776 [math.CO], 2025. See p. 4.
R. J. Mathar, Tiling n x m rectangles with 1 x 1 and s x s squares, arXiv:1609.03964 [math.CO], 2016.
Johan Nilsson, On Counting the Number of Tilings of a Rectangle with Squares of Size 1 and 2, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.2.

Columns (or rows) k=0+1,2-10 give: A000012, A000045(n+1), A001045(n+1), A054854, A054855, A063650, A063651, A063652, A063653, A063654.

Main diagonal gives A063443.

b:= proc(n, l) option remember; local m, k; m:= min(l[]);
      if m>0 then b(n-m, map(x->x-m, l))
    elif n=0 then 1
    else for k while l[k]>0 do od; b(n, subsop(k=1, l))+
         `if`(n>1 and k `if`(min(n, k)<2, 1, b(max(n, k), [0$min(n, k)])):
seq(seq(A(n, d-n), n=0..d), d=0..14);

b[n_, l_] := b[n, l] = Module[{m=Min[l], k}, If[m>0, b[n-m, l-m], If[n == 0, 1, k=Position[l, 0, 1, 1][[1, 1]]; b[n, ReplacePart[l, k -> 1]] + If[n>1 && k 2, k+1 -> 2}]], 0]]]]; A[n_, k_] := If[Min[n, k]<2, 1, b[Max[n, k], Table[0, {Min[n, k]}]]]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-François Alcover, Dec 11 2014, after Alois P. Heinz *)

A067958 Number of binary arrangements without adjacent 1's on n X n torus connected e-w ne-sw n-s nw-se.

Original entry on oeis.org

1, 5, 10, 133, 1411, 42938, 1796859, 157763829, 22909432780, 6291183426165, 3032485231813445, 2674030233698391466, 4216437656471537450175, 12038380931111061789962901, 61810608197507432888286102310, 572863067272579464080483552434421

Offset: 1

R. H. Hardin, Feb 02 2002

For n > 1, a(n) is also the number of ways to populate an n X n toroidal chessboard with non-attacking kings (including the case of zero kings). - Vaclav Kotesovec, Oct 10 2011

			Neighbors for n=4:
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\
  :\|/\|/\|/\|/
  :-o--o--o--o-
  :/|\/|\/|\/|\

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 214.

Cf. circle A000204, line A000045, arrays: ne-sw nw-se A067965, e-w ne-sw nw-se A067963, n-s nw-se A067964, e-w n-s nw-se A066864, e-w ne-sw n-s nw-se A063443, n-s A067966, e-w n-s A006506, nw-se A067962, toruses: bare A002416, ne-sw nw-se A067960, ne-sw n-s nw-se A067959, n-s A067961, e-w n-s A027683, e-w ne-sw n-s A066866.

Cf. A212269.

a(14) from Vaclav Kotesovec, Aug 22 2016

a(15)-a(16) from Vaclav Kotesovec, May 15 2021

cp's OEIS Frontend

A247413 Decimal expansion of the entropy constant related to A063443.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Formula

A045846 Number of distinct ways to cut an n X n square into squares with integer sides.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A067966 Number of binary arrangements without adjacent 1's on n X n array connected n-s.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

PARI

Formula

Extensions

A067961 Number of binary arrangements without adjacent 1's on n X n torus connected n-s.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula

Extensions

A067965 Number of binary arrangements without adjacent 1's on n X n array connected ne-sw and nw-se.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

A193580 Triangle read by rows: T(n,k) = number of ways to place k nonattacking kings on an n X n board.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Formula

A067960 Number of binary arrangements without adjacent 1's on n X n torus connected ne-sw nw-se.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A067962 a(n) = F(n+2)*(Product_{i=1..n+1} F(i))^2 where F(i)=A000045(i) is the i-th Fibonacci number.

Views

Author