cp's OEIS Frontend

A231473 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=floor(n/3), read by rows.

%I A231473 #32 Oct 06 2017 08:36:20
%S A231473 1,2,1,2,1,4,1,4,4,1,6,9,1,6,18,1,8,28,10,1,8,42,28,1,10,57,76,1,10,
%T A231473 76,140,25,1,12,96,254,107,1,12,120,392,321,1,14,145,600,731,70,1,14,
%U A231473 174,840,1462,366,1,16,204,1170,2610,1308,1,16,238,1540,4350,3416,196
%N A231473 Number T(n,k) of equivalence classes of ways of placing k 3 X 3 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=3, 0<=k<=floor(n/3), read by rows.
%H A231473 Andrew Howroyd, <a href="/A231473/b231473.txt">Table of n, a(n) for n = 3..974</a>
%H A231473 Christopher Hunt Gribble, <a href="/A238009/a238009_1.cpp.txt">C++ program</a>
%e A231473 The first 11 rows of T(n,k) are:
%e A231473 .\ k    0      1      2      3      4
%e A231473 n
%e A231473 3       1      2
%e A231473 4       1      2
%e A231473 5       1      4
%e A231473 6       1      4      4
%e A231473 7       1      6      9
%e A231473 8       1      6     18
%e A231473 9       1      8     28     10
%e A231473 10      1      8     42     28
%e A231473 11      1     10     57     76
%e A231473 12      1     10     76    140     25
%e A231473 13      1     12     96    254    107
%t A231473 T[n_, k_] := ((3^k + 1)*Binomial[n - 2k, k] + Boole[EvenQ[k] || OddQ[n]]*(3^(Quotient[(k + 1), 2]) + 3^Quotient[k, 2]) Binomial[(n - 2k - Mod[n, 2])/2, Quotient[k, 2]])/4; Table[T[n, k], {n, 3, 20}, {k, 0, Floor[n/3]}] // Flatten (* _Jean-François Alcover_, Oct 06 2017, after _Andrew Howroyd_ *)
%o A231473 (C++) See Gribble link.
%o A231473 (PARI)
%o A231473 T(n,k)={((3^k+1)*binomial(n-2*k,k) + (k%2==0||n%2==1) * (3^((k+1)\2)+3^(k\2)) * binomial((n-2*k-(n%2))/2,k\2))/4}
%o A231473 for(n=3,20,for(k=0,floor(n/3), print1(T(n,k), ", "));print) \\ _Andrew Howroyd_, May 29 2017
%Y A231473 Cf. A034851, A226048, A102541, A226290, A238009, A228570, A225812, A238189, A238190, A228572, A228022, A231145, A231568, A232440, A228165, A238550-A238552, A228166, A238555, A238556, A228167, A238557-A238559, A228168, A238581-A238583, A228169, A238586, A238592.
%K A231473 tabf,nonn
%O A231473 3,2
%A A231473 _Christopher Hunt Gribble_, Feb 23 2014
%E A231473 Terms corrected and xrefs updated by _Christopher Hunt Gribble_, Apr 26 2015
%E A231473 Terms a(40) and beyond from _Andrew Howroyd_, May 29 2017