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 A238552 Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 6 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, 2, 1, 2, 1, 4, 1, 4, 1, 6, 4, 1, 6, 9, 1, 8, 18, 1, 8, 28, 1, 10, 42, 10, 1, 10, 57, 28, 1, 12, 76, 76, 1, 12, 96, 140, 1, 14, 120, 254, 25, 1, 14, 145, 392, 107, 1, 16, 174, 600, 321, 1, 16, 204, 840, 731, 1, 18, 238, 1170, 1462, 70, 1, 18, 273, 1540, 2610, 366 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 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      2 5       1      2 6       1      4 7       1      4 8       1      6      4 9       1      6      9 10      1      8     18 11      1      8     28 12      1     10     42     10 13      1     10     57     28 14      1     12     76     76 15      1     12     96    140 16      1     14    120    254    25 17      1     14    145    392   107 MATHEMATICA T[n_, k_] := ((3^k + 1) Binomial[n - 3k, k] + Boole[EvenQ[k] || EvenQ[n]]*(3^Quotient[k + 1, 2] + 3^Quotient[k, 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)={((3^k+1)*binomial(n-3*k, k) + (k%2==0||n%2==0) * (3^((k+1)\2)+3^(k\2)) * binomial((n-3*k-(k%2)-(n%2))/2, k\2))/4} for(n=4, 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, A231568, A232440, A228165, A238550, A238551,  A228166, A238555, A238556, A228167, A238557, A238558, A238559, A228168, A238581, A238582, A238583, A228169, A238586, A238592. Sequence in context: A193787 A072614 A287597 * A257523 A067044 A325677 Adjacent sequences:  A238549 A238550 A238551 * A238553 A238554 A238555 KEYWORD tabf,nonn AUTHOR Christopher Hunt Gribble, Feb 28 2014 EXTENSIONS Terms corrected and xrefs updated by Christopher Hunt Gribble, Apr 27 2015 Terms a(28) and beyond from Andrew Howroyd, May 29 2017 STATUS approved

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Last modified February 23 13:37 EST 2020. Contains 332159 sequences. (Running on oeis4.)