A067966 -id:A067966 - cp's OEIS frontend

A197989 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected n-s.

1, 4, 45, 886, 24395, 860336, 36914493, 1863645610, 108131503623, 7085585223652, 517329551346608, 41634263983867842, 3661077644199252550, 349191617521920855488, 35902782820742394839453, 3958207187579046500083794, 465777357329812920074875295

Offset: 1

Vaclav Kotesovec, Oct 20 2011

Vaclav Kotesovec, Table of n, a(n) for n = 1..108
V. Kotesovec, Non-attacking chess pieces, 6ed, p.373-381

Cf. A067966, A197990.

permopak[part_,k_]:=(hist=ConstantArray[0,k];
Do[hist[[part[[t]]]]++,{t,1,Length[part]}];
(Length[part])!/Product[(hist[[t]])!,{t,1,k}]);
waz1n[k_,n_]:=(If[n-k+1

Asymptotic (V. Kotesovec, Oct 15 2011): a(n) ~ n^(2n)/n!*exp(-3/2).

A210343 a(n) = Fibonacci(n+1)^n.

Original entry on oeis.org

1, 1, 4, 27, 625, 32768, 4826809, 1801088541, 1785793904896, 4605366583984375, 31181719929966183601, 552061438912436417593344, 25601832525455335435322705761, 3107689015140868348741078056241817, 987683253336131809511244100000000000000

Offset: 0

Emanuele Munarini, Mar 20 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..70

Cf. A100399, A067966, A210341, A210342.

[Fibonacci(n+1)^n: n in [0..14]]; // Bruno Berselli, Mar 28 2012

a:= n-> (<<1|1>, <1|0>>^n)[1,1]^n:
seq(a(n), n=0..15);  # Alois P. Heinz, Dec 05 2015

Mathematica
```
Table[Fibonacci[n+1]^n,{n,0,100}]
```
Maxima
```
makelist(fib(n+1)^n,n,0,14);
```

A182562 Number of ways to place k non-attacking semi-knights on an n x n chessboard, sum over all k>=0.

Original entry on oeis.org

2, 16, 288, 11664, 1458000, 506250000, 414720000000, 869730877440000, 5045702916833280000, 77297454895962562560000, 3017525202366485003182080000, 307389127582207654481154908160000, 83016370640108703579427655610531840000, 58770343311359208383258439665073059266560000

Offset: 1

Vaclav Kotesovec, May 05 2012

nonn

Semi-knight is a semi-leaper [1,2]. Moves of a semi-knight are allowed only in [2,1] and [-2,-1]. See also semi-bishops (A187235).

Vaclav Kotesovec, Table of n, a(n) for n = 1..60
V. Kotesovec, Non-attacking chess pieces

Cf. A067962, A067966, A063443, A006506, A067965, A066864, A067963, A067964, A182563

Table[If[EvenQ[n],Fibonacci[n/2+2]^(n+2)*Product[Fibonacci[j+2]^4,{j,1,n/2-1}],Fibonacci[(n+1)/2+2]^((n+1)/2)*Fibonacci[(n-1)/2+2]^((n-1)/2)*Product[Fibonacci[j+2]^4,{j,1,(n-1)/2}]],{n,1,20}]

a(n) = F(n/2+2)^(n+2)*prod(j=1,n/2-1,F(j+2)^4) if n is even, F((n+1)/2+2)^((n+1)/2)*F((n-1)/2+2)^((n-1)/2)*prod(j=1,(n-1)/2,F(j+2)^4) if n is odd, where F(n) = A000045(n) is the n-th Fibonacci number.

a(n) is asymptotic to C^4*((1+sqrt(5))/2)^((n+2)*(n+4))/5^(3/2*(n+2)), where C=1.226742010720353244... is Fibonacci Factorial Constant, see A062073.

A201222 Number of ways to place k non-attacking knights on a 2 X n horizontal cylinder, summed over all k>=0.

Original entry on oeis.org

3, 9, 18, 81, 123, 324, 843, 2401, 5778, 15129, 39603, 104976, 271443, 710649, 1860498, 4879681, 12752043, 33385284, 87403803, 228886641, 599074578, 1568397609, 4106118243, 10750371856, 28143753123, 73681302249, 192900153618, 505022001201, 1322157322203

Offset: 1

Vaclav Kotesovec, Nov 28 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
V. Kotesovec, Non-attacking chess pieces

Cf. A189145, A001333, A051927, A006506, A067966.

Table[If[Mod[n,4]==0,LucasL[n/2]^4,LucasL[2n]+1+(-1)^n],{n,1,50}]

cp's OEIS Frontend

A197989 Number of binary arrangements of total n 1's, without adjacent 1's on n X n array connected n-s.

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A210343 a(n) = Fibonacci(n+1)^n.

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A182562 Number of ways to place k non-attacking semi-knights on an n x n chessboard, sum over all k>=0.

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A201222 Number of ways to place k non-attacking knights on a 2 X n horizontal cylinder, summed over all k>=0.

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Mathematica