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

1,5

Comments

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

Links

Table of n, a(n) for n=1..55.

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

Formula

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

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

Example

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;

Crossrefs

Rows sums give A006516. Right border gives A131577.

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

Sequence in context: A353403 A300939 A062941 * A290427 A265759 A057674

Adjacent sequences: A211015 A211016 A211017 * A211019 A211020 A211021

Keyword

nonn,tabl

Author

Omar E. Pol, Sep 24 2012

Status

approved