The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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-François 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

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.

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