A211016 Triangle read by rows: T(n,k) = number of squares and rectangles of area 2^(k-1) after 2^n stages in the toothpick structure of A139250, n>=1, k>=1, assuming the toothpicks have length 2.
0, 0, 4, 8, 12, 4, 40, 52, 12, 4, 168, 212, 52, 12, 4, 680, 852, 212, 52, 12, 4, 2728, 3412, 852, 212, 52, 12, 4, 10920, 13652, 3412, 852, 212, 52, 12, 4, 43688, 54612, 13652, 3412, 852, 212, 52, 12, 4, 174760, 218452, 54612, 13652, 3412, 852, 212, 52, 12, 4
Offset: 1
Examples
For n = 5 in the toothpick structure after 2^5 stages we have that: T(5,1) = 168 is the number of squares of size 1 X 1. T(5,2) = 212 is the number of rectangles of size 1 X 2. T(5,3) = 52 is the total number of squares of size 2 X 2 and of rectangles of size 1 X 4. T(5,4) = 12 is the number of rectangles of size 2 X 4. T(5,5) = 4 is the number of rectangles of size 2 X 8. Triangle begins: 0; 0, 4; 8, 12, 4; 40, 52, 12, 4; 168, 212, 52, 12, 4; 680, 852, 212, 52, 12, 4; 2728, 3412, 852, 212, 52, 12, 4; 10920, 13652, 3412, 852, 212, 52, 12, 4; 43688, 54612, 13652, 3412, 852, 212, 52, 12, 4; 174760, 218452, 54612, 13652, 3412, 852, 212, 52, 12, 4;
Links
- N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
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