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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: A130542 A128502 A349382 * A345199 A079159 A192298

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

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)