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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244306 Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing two 1 X 1 tiles in an n X k rectangle under all symmetry operations of the rectangle. 6
0, 1, 1, 2, 3, 2, 4, 6, 6, 4, 6, 10, 13, 10, 6, 9, 15, 22, 22, 15, 9, 12, 21, 34, 36, 34, 21, 12, 16, 28, 48, 56, 56, 48, 28, 16, 20, 36, 65, 78, 88, 78, 65, 36, 20, 25, 45, 84, 106, 123, 123, 106, 84, 45, 25, 30, 55, 106, 136, 168, 171, 168, 136, 106, 55, 30 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Christopher Hunt Gribble, Table of n, a(n) for n = 1..9870

FORMULA

Empirically,

T(n,k) = (4*k^2*n^2 + 2*k^2 + 8*k*n + 2*n^2 - 4*k - 4*n - 1 - (2*k^2 - 4*k - 1)*(-1)^n - (2*n^2 - 4*n - 1)*(-1)^k - (-1)^k*(-1)^n)/32.

T(1,k) = A002620(k) = floor(k^2/4).

T(2,k) = A000217(k) = k*(k+1)/2.

       = T(1,k) + T(1,k+1) = floor(k^2/4) + floor((k+1)^2/4).

T(3,k) = 2*A000217(k) + A024206(k-2)

       = k*(k+1) + floor((k-1)^2/4) - 1.

EXAMPLE

T(n,k) for 1<=n<=11 and 1<=k<=11 is:

    k  1    2    3    4    5    6    7    8    9   10   11 ...

.n

.1     0    1    2    4    6    9   12   16   20   25   30

.2     1    3    6   10   15   21   28   36   45   55   66

.3     2    6   13   22   34   48   65   84  106  130  157

.4     4   10   22   36   56   78  106  136  172  210  254

.5     6   15   34   56   88  123  168  216  274  335  406

.6     9   21   48   78  123  171  234  300  381  465  564

.7    12   28   65  106  168  234  321  412  524  640  777

.8    16   36   84  136  216  300  412  528  672  820  996

.9    20   45  106  172  274  381  524  672  856 1045 1270

10    25   55  130  210  335  465  640  820 1045 1275 1550

11    30   66  157  254  406  564  777  996 1270 1550 1885

CROSSREFS

Cf. A034851, A226048, A226290, A225812, A228022, A228165, A228166, A243866, A006918, A244307, A248011, A248016, A248059, A248060, A248017, A248027.

Sequence in context: A062068 A130542 A128502 * A079159 A192298 A254967

Adjacent sequences:  A244303 A244304 A244305 * A244307 A244308 A244309

KEYWORD

tabl,nonn

AUTHOR

Christopher Hunt Gribble, Jun 25 2014

EXTENSIONS

Terms corrected and extended by Christopher Hunt Gribble, Apr 02 2015

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)