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A231568 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=floor(n/4), read by rows. 21
1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 3, 4, 1, 4, 8, 1, 4, 12, 1, 5, 18, 3, 1, 5, 24, 8, 1, 6, 32, 22, 1, 6, 40, 40, 1, 7, 50, 73, 6, 1, 7, 60, 112, 22, 1, 8, 72, 172, 66, 1, 8, 84, 240, 146, 1, 9, 98, 335, 292, 10, 1, 9, 112, 440, 516, 48, 1, 10, 128, 578, 860, 174 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 4..989

Christopher Hunt Gribble, C++ program

EXAMPLE

The first 14 rows of T(n,k) are:

.\  k    0      1      2      3     4

n

4        1      1

5        1      1

6        1      2

7        1      2

8        1      3      2

9        1      3      4

10       1      4      8

11       1      4     12

12       1      5     18      3

13       1      5     24      8

14       1      6     32     22

15       1      6     40     40

16       1      7     50     73     6

17       1      7     60    112    22

MATHEMATICA

T[n_, k_] := (2^k Binomial[n - 3k, k] + (Boole[EvenQ[k]] + Boole[EvenQ[n] || EvenQ[k]] + Boole[k == 0]) 2^Quotient[k+1, 2] Binomial[(n - 3k - Mod[k, 2] - Mod[n, 2])/2, Quotient[k, 2]])/4; Table[T[n, k], {n, 4, 20}, {k, 0, Floor[n/4]}] // Flatten (* Jean-Fran├žois Alcover, Oct 06 2017, after Andrew Howroyd *)

PROG

(C++) See Gribble link.

(PARI)

T(n, k)={(2^k*binomial(n-3*k, k) + ((k%2==0)+(n%2==0||k%2==0)+(k==0)) * 2^((k+1)\2)*binomial((n-3*k-(k%2)-(n%2))/2, k\2))/4}

for(n=2, 20, for(k=0, floor(n/4), print1(T(n, k), ", ")); print) \\ Andrew Howroyd, May 29 2017

CROSSREFS

Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231473, A232440, A228165, A238550, A238551, A238552, A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592.

Sequence in context: A191476 A134583 A087467 * A327525 A327540 A227687

Adjacent sequences:  A231565 A231566 A231567 * A231569 A231570 A231571

KEYWORD

tabf,nonn

AUTHOR

Christopher Hunt Gribble, Feb 23 2014

EXTENSIONS

Terms extended and xrefs updated by Christopher Hunt Gribble, Apr 26 2015

Terms a(32) and beyond from Andrew Howroyd, May 29 2017

STATUS

approved

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Last modified February 19 00:54 EST 2020. Contains 332028 sequences. (Running on oeis4.)