Revision History for A100316
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
| older changes
|
| |
|
| A100316
|
|
Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
(history;
published version)
|
| |
|
|
#24 by N. J. A. Sloane at Thu Feb 09 21:58:08 EST 2023
| |
| |
| |
|
|
#23 by Michel Marcus at Thu Feb 02 00:48:00 EST 2023
| |
| |
| |
|
|
#22 by Michel Marcus at Thu Feb 02 00:47:54 EST 2023
|
|
| LINKS
|
S. Sergey Kitaev, <a href="http://www.emis.de/journals/INTEGERS/papers/e21/e21.Abstract.html">On multi-avoidance of right angled numbered polyomino patterns</a>, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
|
|
| STATUS
|
proposed
editing
|
| |
| |
|
|
#21 by G. C. Greubel at Wed Feb 01 15:42:19 EST 2023
| |
| |
| |
|
|
#20 by G. C. Greubel at Wed Feb 01 15:41:52 EST 2023
|
|
| COMMENTS
|
An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1< < i2, j1< < j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by 2^m+ + 2^n+ + 2(nm*(n*m-n-m).
|
|
| LINKS
|
G. C. Greubel, <a href="/A100316/b100316.txt">Table of n, a(n) for n = 0..1000</a>
<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -,-5, ,2).
|
|
| FORMULA
|
G.f.: -(16.: (1+12*x^3-35*x^2+1216*x+1^3)/((1-2*x-1)*(x-1-x)^2). - Alois P. Heinz, Dec 21 2018
E.g.f.: exp(2*x) + 2*(4+3*x)*exp(x) - 8. - G. C. Greubel, Feb 01 2023
|
|
| MATHEMATICA
|
Table[If[6*n + ==0, 1, 2^n+6*n + +8, {], {n, , 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)
|
|
| PROG
|
(Magma) [2^n+6*n+8*(1-0^n): n in [0..40]]; // G. C. Greubel, Feb 01 2023
(SageMath) [2^n+6*n+8*(1-0^n) for n in range(41)] # G. C. Greubel, Feb 01 2023
|
|
| CROSSREFS
|
Cf. A100314 (m=2), A100315 (m=3), this sequence (m=4).
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#19 by Alois P. Heinz at Fri Dec 21 17:53:15 EST 2018
| |
| |
| |
|
|
#18 by Alois P. Heinz at Fri Dec 21 17:52:47 EST 2018
|
|
| FORMULA
|
G.f.: -(16*x^3-35*x^2+12*x+1)/((2*x-1)*(x-1)^2). - Alois P. Heinz, Dec 21 2018
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
#17 by Alois P. Heinz at Fri Dec 21 17:50:53 EST 2018
| |
| |
| |
|
|
#16 by Alois P. Heinz at Fri Dec 21 17:50:31 EST 2018
|
|
| FORMULA
|
a(n) = 2^n + 6*n + 8 for n>0, a(0) = 1.
|
| |
| |
|
|
#15 by Alois P. Heinz at Fri Dec 21 17:48:56 EST 2018
|
|
| DATA
|
1, 16, 24, 34, 48, 70, 108, 178, 312, 574, 1092, 2122, 4176, 8278, 16476, 32866, 65640, 131182, 262260, 524410, 1048704, 2097286, 4194444, 8388754, 16777368, 33554590, 67109028, 134217898, 268435632, 536871094, 1073742012, 2147483842, 4294967496, 8589934798
|
|
| OFFSET
|
1,1
0,2
|
|
| AUTHOR
|
_Sergey Kitaev (kitaev(AT)ms.uky.edu), _, Nov 13 2004
|
|
| EXTENSIONS
|
a(0)=1 prepended by Alois P. Heinz, Dec 21 2018
|
|
| STATUS
|
approved
editing
|
| |
| |
|
|
