Brian Kell has authored 4 sequences.
A253316
Number of 2n X 2n Takuzu grids.
Original entry on oeis.org
1, 2, 72, 4140, 4111116, 48183195384
Offset: 0
The following is a 4 X 4 Takuzu grid:
[ 0 1 1 0 ]
[ 1 0 0 1 ]
[ 0 0 1 1 ]
[ 1 1 0 0 ]
Number of possible rows equals
A003440.
A145835
Number of compositions of the n X n grid graph.
Original entry on oeis.org
1, 12, 1434, 1691690, 19719299768, 2271230282824746, 2584855762327078145444, 29068227444022728740767607050, 3230042572278849047360048508956727420, 3546545075986984198328715750838554116235343894
Offset: 1
For n=2 the a(2)=12 partitions of a 2x2 square are: 1 partition into a single 2x2 region; 4 partitions into a 3-square 'L' shape and an isolated corner; 2 partitions into 2 1x2 bricks; 4 partitions into a 1x2 brick and 2 isolated squares; and 1 partition into 4 isolated squares.
- A. Knopfmacher and M. E. Mays, Graph compositions I: Basic enumeration, Integers, 1 (2001), #A4.
- J. N. Ridley and M. E. Mays, Compositions of unions of graphs, Fib. Quart., 42 (2004), 222-230.
- Frank Simon, Algebraic Methods for Computing the Reliability of Networks, Dissertation, Doctor Rerum Naturalium (Dr. rer. nat.), Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden, 2012. - From _N. J. A. Sloane_, Jan 04 2013
A099350
Numbers k such that 4*k! - 1 is prime.
Original entry on oeis.org
0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579, 1264, 2276, 2669, 4316, 4382, 4678, 7907, 10843
Offset: 1
k = 5 is here because 4*5! - 1 = 479 is prime.
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for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;
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For[n = 0, True, n++, If[PrimeQ[4 n! - 1], Print[n]]] (* Jean-François Alcover, Sep 23 2015 *)
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is_A099350(n)=ispseudoprime(n!*4-1) \\ M. F. Hasler, Sep 20 2015
A099351
Numbers k such that 5*k! - 1 is prime.
Original entry on oeis.org
3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521, 1279, 1750, 2204, 2473, 4193, 5181, 10080
Offset: 1
k = 5 is here because 5*5! - 1 = 599 is prime.
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for n from 0 to 1000 do if isprime(5*n! - 1) then print(n) end if end do;
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Select[Range[550],PrimeQ[5#!-1]&] (* Harvey P. Dale, Nov 27 2013 *)
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is(n)=ispseudoprime(5*n!-1) \\ Charles R Greathouse IV, Jun 13 2017
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from sympy import isprime
from math import factorial
print([k for k in range(300) if isprime(5*factorial(k) - 1)]) # Michael S. Branicky, Mar 05 2021
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