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Search: id:A151567
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| A151567 |
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Another version of the toothpick sequence A139250 (see Comments for definition). |
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+0
1
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| 0, 1, 3, 7, 11, 15, 23, 35, 43, 47, 55, 67, 79, 91, 111, 139, 155, 159, 167, 179, 191, 203, 223, 251, 271, 283, 303, 331, 359, 387, 431, 491, 523, 527, 535, 547, 559, 571, 591, 619, 639, 651, 671, 699, 727, 755, 799, 859, 895, 907, 927, 955, 983, 1011, 1055, 1115, 1159, 1187
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The idea is to build a version of A139250 from four copies of the triangle in A151566 (each rotated from the previous one by 90 degrees). The result doesn't quite match A139250, however.
The toothpicks here have length 2, and are placed on the square grid Z X Z.
Place a vertical toothpick centered at (0,0) and extend it downwards to form an infinite triangle using the rule for leftist trees in A151566.
Place another vertical toothpick centered at (0,0) and extend it upwards to form an infinite triangle using the rule for leftist trees in A151566.
Place a horizontal toothpick centered at (1,0) and extend it leftwards to form an infinite triangle using the rule for leftist trees in A151566, then remove the toothpick centered at (1,0).
Place another horizontal toothpick centered at (-1,0) and extend it rightwards to form an infinite triangle using the rule for leftist trees in A151566, then remove the toothpick centered at (-1,0).
Finally, coalesce any toothpicks that have been superimposed. The result starts like A139250, but after 12 generations has fewer toothpicks.
The sequence gives the number of toothpicks in the n-th generation.
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FORMULA
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a(n) = 2*P(n) + 2*P(n+1) -4*n - 1, where P() = A151566().
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CROSSREFS
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Sequence in context: A036994 A112714 A160808 this_sequence A139250 A145052 A100900
Adjacent sequences: A151564 A151565 A151566 this_sequence A151568 A151569 A151570
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 24 2009
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