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A262616 Triangle read by rows: T(n,k) = 4^(n-k), n>=0, 0<=k<=n.

%I A262616 #27 Feb 13 2017 16:23:16
%S A262616 1,4,1,16,4,1,64,16,4,1,256,64,16,4,1,1024,256,64,16,4,1,4096,1024,
%T A262616 256,64,16,4,1,16384,4096,1024,256,64,16,4,1,65536,16384,4096,1024,
%U A262616 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 A262616 Triangle read by rows: T(n,k) = 4^(n-k), n>=0, 0<=k<=n.
%C A262616 A triangle of the same family of A130321 and A140303, with the same offset.
%C A262616 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 A262616 Indranil Ghosh, <a href="/A262616/b262616.txt">Rows 0..100, flattened</a>
%H A262616 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 A262616 T(n,k) = A000302(n-k).
%e A262616 Triangle begins:
%e A262616 1;
%e A262616 4,       1;
%e A262616 16,      4,       1;
%e A262616 64,      16,      4,      1;
%e A262616 256,     64,      16,     4,     1;
%e A262616 1024,    256,     64,     16,    4,     1;
%e A262616 4096,    1024,    256,    64,    16,    4,    1;
%e A262616 16384,   4096,    1024,   256,   64,    16,   4,    1;
%e A262616 65536,   16384,   4096,   1024,  256,   64,   16,   4,   1;
%e A262616 262144,  65536,   16384,  4096,  1024,  256,  64,   16,  4,  1;
%e A262616 1048576, 262144,  65536,  16384, 4096,  1024, 256,  64,  16, 4,  1;
%e A262616 4194304, 1048576, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;
%e A262616 ...
%t A262616 Table[4^(n - k), {n, 0, 10}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Jul 17 2016 *)
%Y A262616 Column k gives A000302.
%Y A262616 Row sums give the positive terms of A002450.
%Y A262616 Alternating row sums give the positive terms of A015521.
%Y A262616 Cf. A130321, A139250, A140303, A152571, A152716.
%K A262616 nonn,tabl,easy
%O A262616 0,2
%A A262616 _Omar E. Pol_, Nov 23 2015