A211018 Triangle read by rows: T(n,k) = total area of all squares and rectangles of area 2^(k-1) after 2^n stages in the toothpick structure of A139250, divided by 8, n>=1, k>=1, assuming the toothpicks have length 2.

0, 0, 1, 1, 3, 2, 5, 13, 6, 4, 21, 53, 26, 12, 8, 85, 213, 106, 52, 24, 16, 341, 853, 426, 212, 104, 48, 32, 1365, 3413, 1706, 852, 424, 208, 96, 64, 5461, 13653, 6826, 3412, 1704, 848, 416, 192, 128, 21845, 54613, 27306, 13652, 6824, 3408, 1696, 832, 384, 256

Offset: 1

Author

Omar E. Pol, Sep 24 2012

Keywords

• nonn
• tabl

Comments

All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.

Examples

			0;
0,        1;
1,        3,    2;
5,       13,    6,    4;
21,      53,   26,   12,    8;
85,     213,  106,   52,   24,  16;
341,    853,  426,  212,  104,  48,  32;
1365,  3413, 1706,  852,  424, 208,  96,  64;
5461, 13653, 6826, 3412, 1704, 848, 416, 192, 128;
		

Links

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

Crossrefs

Rows sums give A006516. Right border gives A131577.

Cf. A002450, A072197, A139250, A160124, A211012, A211016, A211017, A211019

Formula

T(n,k) = A211017(n,k)/8.

T(n,1) = A002450(n-2), n>=2.