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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
OFFSET
5,6
LINKS
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
KEYWORD
tabf,nonn
AUTHOR
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