|
%I #74 Sep 16 2020 02:20:42
%S 1,1,1,1,2,1,1,1,1,4,2,1,2,1,1,1,1,2,1,4,8,2,2,1,1,4,2,1,2,1,1,1,1,2,
%T 1,2,4,1,1,4,4,16,8,2,4,2,2,1,1,2,1,4,8,2,2,1,1,4,2,1,2,1,1,1,1,2,1,2,
%U 4,1,1,2,2,8,4,1,2,1,1,4,4,8,4,16,32,8
%N Row lengths of irregular triangle A335967.
%C All terms are powers of 2.
%H Rémy Sigrist, <a href="/A337131/a337131.gp.txt">PARI program for A337131</a>
%F a(2^k-1) = 1 for any k >= 0.
%F a(2^k) = 1 for any k >= 0.
%F a(A000975(k)) = 2^(k-2) for any k >= 2.
%e For n = 13, the binary representation of 13 is "1101", so we consider the tilings of a size 4 staircase polyomino whose base has the following shape:
%e .....
%e . .
%e . .....
%e . .
%e +---+ .....
%e | | .
%e | +---+---+---+
%e | 1 1 | 0 | 1 |
%e +-------+---+---+
%e There are two possible penultimate rows:
%e ..... .....
%e . . . .
%e . ..... . .....
%e . | . . .
%e +---+ +---+ +---+---+---+
%e | 1 | 0 0 | | 1 | 0 | 1 |
%e | +---+---+---+ | +---+---+---+
%e | | | | | | | |
%e +-------+---+---+, +-------+---+---+
%e so a(13) = 2.
%o (PARI) See Links section.
%Y Cf. A000975, A335967.
%K nonn
%O 1,5
%A _Rémy Sigrist_, Sep 14 2020
|
