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A262616 Triangle read by rows: T(n,k) = 4^(n-k), n>=0, 0<=k<=n. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Indranil Ghosh, Rows 0..100, flattened

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

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

EXAMPLE

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;

...

MATHEMATICA

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

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.

Sequence in context: A059222 A117292 A062780 * A309074 A175844 A167343

Adjacent sequences:  A262613 A262614 A262615 * A262617 A262618 A262619

KEYWORD

nonn,tabl,easy

AUTHOR

Omar E. Pol, Nov 23 2015

STATUS

approved

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Last modified February 24 01:16 EST 2020. Contains 332195 sequences. (Running on oeis4.)