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

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

Offset: 0

Author

Omar E. Pol, Nov 23 2015

Keywords

• nonn
• tabl
• easy

Comments

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

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.

Examples

			Triangle begins:
1;
4,       1;
16,      4,       1;
64,      16,      4,      1;
256,     64,      16,     4,     1;
1024,    256,     64,     16,    4,     1;
4096,    1024,    256,    64,    16,    4,    1;
16384,   4096,    1024,   256,   64,    16,   4,    1;
65536,   16384,   4096,   1024,  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;
4194304, 1048576, 262144, 65536, 16384, 4096, 1024, 256, 64, 16, 4, 1;
...
		

Links

• Indranil Ghosh, Rows 0..100, flattened
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Column k gives A000302.

Row sums give the positive terms of A002450.

Alternating row sums give the positive terms of A015521.

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

Programs

Mathematica

Table[4^(n - k), {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jul 17 2016 *)

Formula

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