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.

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

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: A344233 A072625 A268187 * A355749 A278538 A282903

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