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A211016
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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.
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6
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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
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OFFSET
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1,3
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COMMENTS
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All internal regions in the toothpick structure are squares and rectangles.
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LINKS
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FORMULA
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EXAMPLE
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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;
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CROSSREFS
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Row sums give 0 together with A145655.
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KEYWORD
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AUTHOR
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STATUS
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approved
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