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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
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.
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.
Sequence in context: A059222 A117292 A062780 * A309074 A175844 A351434
KEYWORD
nonn,tabl,easy
AUTHOR
Omar E. Pol, Nov 23 2015
STATUS
approved