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 A232440 Number T(n,k) of equivalence classes of ways of placing k 5 X 5 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=5, 0<=k<=floor(n/5), read by rows. 21
 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 4, 2, 1, 4, 4, 1, 5, 6, 1, 5, 9, 1, 6, 12, 1, 1, 6, 16, 2, 1, 7, 20, 6, 1, 7, 25, 10, 1, 8, 30, 19, 1, 8, 36, 28, 1, 1, 9, 42, 44, 3, 1, 9, 49, 60, 9, 1, 10, 56, 85, 19, 1, 10, 64, 110, 38, 1, 11, 72, 146, 66, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,6 LINKS Andrew Howroyd, Table of n, a(n) for n = 5..989 Christopher Hunt Gribble, C++ program EXAMPLE The first 9 rows of T(n,k) are: .\ k    0      1      2 n 5       1      1 6       1      1 7       1      2 8       1      2 9       1      3 10      1      3      1 11      1      4      2 12      1      4      4 13      1      5      6 MATHEMATICA T[n_, k_] := (Binomial[n - 4k, k] + Boole[EvenQ[k] || OddQ[n]] Binomial[(n - 4k - Mod[n, 2])/2, Quotient[k, 2]])/2; Table[T[n, k], {n, 5, 20}, {k, 0, Quotient[n, 5]}] // Flatten (* Jean-François Alcover, Oct 06 2017, after Andrew Howroyd *) PROG (C++) See Gribble link. (PARI) T(n, k)={(binomial(n-4*k, k) + (k%2==0||n%2==1)*binomial((n-4*k-n%2)/2, k\2))/2} for(n=5, 20, for(k=0, (n\5), 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, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586, A238592. Sequence in context: A137163 A072625 A268187 * A278538 A282903 A332677 Adjacent sequences:  A232437 A232438 A232439 * A232441 A232442 A232443 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(27) and beyond from Andrew Howroyd, May 29 2017 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)