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A238009 Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 3 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=floor(n/2), read by rows. 23
1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 1, 3, 8, 3, 1, 3, 12, 8, 1, 4, 18, 22, 6, 1, 4, 24, 40, 22, 1, 5, 32, 73, 66, 10, 1, 5, 40, 112, 146, 48, 1, 6, 50, 172, 292, 174, 20, 1, 6, 60, 240, 516, 448, 116, 1, 7, 72, 335, 860, 1020, 464, 36, 1, 7, 84, 440, 1340, 2016, 1360, 256 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,6

LINKS

Christopher Hunt Gribble and Andrew Howroyd, Rows n=2..60 of T(n,k) flattened (Rows n=2..20 from Christopher Hunt Gribble)

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 19 rows of T(n,k) are:

   n\k 0  1   2    3    4     5     6     7     8    9  10

   2   1  1

   3   1  1

   4   1  2   2

   5   1  2   4

   6   1  3   8    3

   7   1  3  12    8

   8   1  4  18   22    6

   9   1  4  24   40   22

  10   1  5  32   73   66    10

  11   1  5  40  112  146    48

  12   1  6  50  172  292   174    20

  13   1  6  60  240  516   448   116

  14   1  7  72  335  860  1020   464    36

  15   1  7  84  440 1340  2016  1360   256

  16   1  8  98  578 2010  3716  3400  1168    72

  17   1  8 112  728 2890  6336  7432  3840   584

  18   1  9 128  917 4046 10326 14864 10600  2920  136

  19   1  9 144 1120 5502 16016 27536 25344 10600 1280

  20   1 10 162 1368 7336 24066 48188 54992 31800 7080 272

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={(2^k*binomial(n-1*k, k) + ((k%2==0)+(n%2==0||k%2==0)+(k==0)) * 2^((k+1)\2)*binomial((n-1*k-(k%2)-(n%2))/2, k\2))/4}

for(n=2, 20, for(k=0, floor(n/2), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A231568, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

Sequence in context: A021456 A125912 A127677 * A231145 A007427 A048106

Adjacent sequences:  A238006 A238007 A238008 * A238010 A238011 A238012

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 16 2014

EXTENSIONS

Corrected C++ program and xrefs added by Christopher Hunt Gribble, Apr 25 2015

STATUS

approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)