A170892
Toothpick sequence similar to A160406, but always staying outside the wedge, starting at stage 1 with a vertical toothpick whose endpoint touches the vertex of the wedge.
Original entry on oeis.org
0, 1, 2, 4, 8, 12, 16, 24, 34, 44, 48, 56, 66, 78, 90, 112, 138, 156, 160, 168, 178, 190, 202, 224, 250, 270, 282, 304, 332, 364, 406, 472, 538, 572, 576, 584, 594, 606, 618, 640, 666, 686, 698, 720, 748, 780, 822, 888, 954, 990, 1002, 1024, 1052, 1084, 1126, 1192, 1260, 1308, 1350, 1418, 1502, 1604, 1750, 1944
Offset: 0
-
A170892(n, print_all=0)={my( ee=[[2*I, I]], p=Set( concat( vector( 2*n-(n>0),k,k-n-abs(k-n)*I ), I )), cnt=2); print_all & print1("1,2"); n<3 & return(n); for(i=3, n, p=setunion(p, Set(Mat(ee~)[, 1])); my(c, d, ne=[]); for( k=1, #ee, setsearch(p, c=ee[k][1]+d=ee[k][2]*I) || ne=setunion(ne, Set([[c, d]])); setsearch(p, c-2*d) || ne=setunion(ne, Set([[c-2*d, -d]]))); forstep( k=#ee=eval(ne), 2, -1, ee[k][1]==ee[k-1][1] & k-- & ee=vecextract(ee, Str("^"k"..", k+1))); cnt+=#ee; print_all & print1(","cnt)); cnt} \\ - M. F. Hasler, Jan 30 2013
A170887
First differences of toothpick sequence A170886.
Original entry on oeis.org
0, 1, 2, 2, 2, 4, 6, 6, 6, 8, 12, 6, 8, 12, 18, 14, 14, 20, 20, 6, 8, 12, 18, 14, 16, 24, 26, 16, 24, 38, 46, 38, 42, 52, 36, 6, 8, 12, 18, 14, 16, 24, 26, 16, 24, 38, 46, 38, 44, 56, 42, 16, 24, 38, 46, 40, 52, 70, 64, 52, 82, 118, 126, 114, 130, 132, 68, 6, 8, 12, 18, 14, 16, 24
Offset: 0
From _Omar E. Pol_, Jan 30 2013: (Start)
If written as an irregular triangle in which rows 0..3 have length 1, it appears that row j has length 2^(j-4), if j >= 4. - _Omar E. Pol_, Jan 31 2013
0;
1;
2;
2;
2;
4,6;
6,6,8,12;
6,8,12,18,14,14,20,20;
6,8,12,18,14,16,24,26,16,24,38,46,38,42,52,36;
6,8,12,18,14,16,24,26,16,24,38,46,38,44,56,42,16,24,38,46,40,52,70,64,52,82,118,126,114,130,132,68;
6,8,12,18,14,16,24,...
(End)
A170889
First differences of toothpick sequence A170888.
Original entry on oeis.org
0, 1, 2, 4, 4, 4, 6, 10, 8, 4, 6, 10, 10, 12, 20, 26, 16, 4, 6, 10, 10, 12, 20, 26, 18, 12, 20, 28, 30, 42, 64, 66, 32, 4, 6, 10, 10, 12, 20, 26, 18, 12, 20, 28, 30, 42, 64, 66, 34, 12, 20, 28, 30, 42, 64, 68, 46, 42, 66, 84, 100, 146, 192, 162, 64, 4, 6, 10, 10, 12, 20, 26, 18, 12
Offset: 0
From _Omar E. Pol_, Jan 30 2013 (Start):
Written as an irregular triangle:
0;
1;
2;
4,4;
4,6,10,8;
4,6,10,10,12,20,26,16;
4,6,10,10,12,20,26,18,12,20,28,30,42,64,66,32;
4,6,10,10,12,20,26,18,12,20,28,30,42,64,66,34,12,20,28,30,42,64,68,46,42,66,84,100,146,192,162,64;
(End)
A170891
First differences of the toothpick sequence A170890.
Original entry on oeis.org
0, 1, 1, 2, 3, 3, 4, 7, 8, 8, 6, 10, 8, 10, 12, 20, 20, 16, 12, 14, 8, 10, 12, 20, 20, 18, 18, 24, 22, 28, 40, 56, 52, 38, 28, 22, 8, 10, 12, 20, 20, 18, 18, 24, 22, 28, 40, 56, 52, 40, 34, 32, 22, 28, 40, 56, 54, 50, 56, 66, 68, 92, 132, 160, 138, 98, 68, 38
Offset: 0
From _Omar E. Pol_, Jan 31 2013 (Start):
If written as an irregular triangle in which rows 0..4 have length 1, it appears that row j has length 2^(j-5), if j >= 5.
0;
1;
1;
2;
3;
3;
4,7;
8,8,6,10;
8,10,12,20,20,16,12,14;
8,10,12,20,20,18,18,24,22,28,40,56,52,38,28,22;
8,10,12,20,20,18,18,24,22,28,40,56,52,40,34,32,22,28,40,56,54,50,56,66,68,92,132,160,138,98,68,38;
(End)
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