A262616 - OEIS

%I #27 Feb 13 2017 16:23:16

%S 1,4,1,16,4,1,64,16,4,1,256,64,16,4,1,1024,256,64,16,4,1,4096,1024,

%T 256,64,16,4,1,16384,4096,1024,256,64,16,4,1,65536,16384,4096,1024,

%U 256,64,16,4,1,262144,65536,16384,4096,1024,256,64,16,4,1,1048576,262144,65536,16384,4096,1024,256,64,16,4,1

%N Triangle read by rows: T(n,k) = 4^(n-k), n>=0, 0<=k<=n.

%C A triangle of the same family of A130321 and A140303, with the same offset.

%C T(n,k) is also the number of hidden crosses of size k+1 formed by squares and rectangles in the toothpick structure of A139250 after 2^(n+2) stages. The last term in every row represents the central cross of the toothpick structure.

%H Indranil Ghosh, <a href="/A262616/b262616.txt">Rows 0..100, flattened</a>

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%F T(n,k) = A000302(n-k).

%e Triangle begins:

%e 1;

%e 4,       1;

%e 16,      4,       1;

%e 64,      16,      4,      1;

%e 256,     64,      16,     4,     1;

%e 1024,    256,     64,     16,    4,     1;

%e 4096,    1024,    256,    64,    16,    4,    1;

%e 16384,   4096,    1024,   256,   64,    16,   4,    1;

%e 65536,   16384,   4096,   1024,  256,   64,   16,   4,   1;

%e 262144,  65536,   16384,  4096,  1024,  256,  64,   16,  4,  1;

%e 1048576, 262144,  65536,  16384, 4096,  1024, 256,  64,  16, 4,  1;

%e 4194304, 1048576, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;

%e ...

%t Table[4^(n - k), {n, 0, 10}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Jul 17 2016 *)

%Y Column k gives A000302.

%Y Row sums give the positive terms of A002450.

%Y Alternating row sums give the positive terms of A015521.

%Y Cf. A130321, A139250, A140303, A152571, A152716.

%K nonn,tabl,easy

%O 0,2

%A _Omar E. Pol_, Nov 23 2015