A170888
Similar to A160406, but always staying outside the wedge, starting at stage 0 with a vertical half-toothpick which protrudes from the vertex of the wedge.
Original entry on oeis.org
0, 1, 3, 7, 11, 15, 21, 31, 39, 43, 49, 59, 69, 81, 101, 127, 143, 147, 153, 163, 173, 185, 205, 231, 249, 261, 281, 309, 339, 381, 445, 511, 543, 547, 553, 563, 573, 585, 605, 631, 649, 661, 681, 709, 739, 781, 845, 911, 945, 957, 977, 1005, 1035, 1077, 1141
Offset: 0
A170893
First differences of the toothpick sequence A170892.
Original entry on oeis.org
0, 1, 1, 2, 4, 4, 4, 8, 10, 10, 4, 8, 10, 12, 12, 22, 26, 18, 4, 8, 10, 12, 12, 22, 26, 20, 12, 22, 28, 32, 42, 66, 66, 34, 4, 8, 10, 12, 12, 22, 26, 20, 12, 22, 28, 32, 42, 66, 66, 36, 12, 22, 28, 32, 42, 66, 68, 48, 42, 68, 84, 102, 146, 194, 162, 66, 4, 8, 10, 12, 12, 22, 26, 20, 12, 22, 28, 32, 42, 66, 66, 36, 12, 22, 28, 32, 42, 66, 68, 48, 42, 68, 84
Offset: 0
From _Omar E. Pol_, Jan 30 2013 (Start):
If written as an irregular triangle in which rows 0..2 have length 1, it appears that row j has length 2^(j-3), if j >= 3.
0;
1;
1;
2;
4,4;
4,8,10,10;
4,8,10,12,12,22,26,18;
4,8,10,12,12,22,26,20,12,22,28,32,42,66,66,34;
4,8,10,12,12,22,26,20,12,22,28,32,42,66,66,36,12,22,28,32,42,66,68,48,42,68,84,102,146,194,162,66;
4,8,10,12,12,22,26,20,12,22,28,32,42,66,66,36,12,22,28,32,42,66,68,48,42,68,84,...
(End)
-
A170893(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 ))); print_all & print1("1,1"); 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))); print_all & print1(","#ee)); (n>0)*#ee} \\ 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)
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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