cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-20 of 20 results.

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

Views

Author

Omar E. Pol, Jan 09 2010

Keywords

Comments

This describes how many toothpicks are added at each step (as to form the upper bar of a T) at all "exposed" endpoints, starting from an initial configuration with a vertical toothpick whose lower endpoint rests on the top of the conic region { (x,y): y < -|x| } into which the toothpicks may not extend. - M. F. Hasler, Jan 30 2013

Examples

			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)

Links

Crossrefs

Cf. A139250, A139251, A160407, A170887, A170889, A170891, A170892.

Programs

  • PARI
    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

Extensions

Values beyond a(10) from 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

Views

Author

Omar E. Pol, Jan 09 2010

Keywords

Comments

Number of toothpicks added at n-th stage to the toothpick structure of A170886. - Omar E. Pol, Jan 31 2013

Examples

			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)

Links

Crossrefs

Cf. A139250, A139251, A160407, A170886, A170889, A170891, A170893.

Extensions

More terms from R. J. Mathar, Jan 25 2010

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

Views

Author

Omar E. Pol, Jan 09 2010

Keywords

Examples

			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)

Links

Crossrefs

Cf. A139250, A139251, A160407, A170887, A170888, A170891, A170893.

Extensions

Terms beyond a(10) from R. J. Mathar, Jan 25 2010

A161833 First differences of A161832.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 4, 2, 2, 2, 4, 3, 4, 5, 9, 5, 2
Offset: 1

Views

Author

Omar E. Pol, Jun 20 2009

Keywords

Comments

Number of Y-toothpicks added to the sieve at the n-th round.

Links

Crossrefs

Cf. A139251, A160121, A160407, A161830, A161831, A161832.

Formula

a(n) = A161831(n+1)/2.

A168113 First differences of A168112.

Original entry on oeis.org

1, 1, 2, 3, 3, 3, 6, 7, 6, 3, 6, 7, 8, 9, 16, 17, 10, 3, 6, 7, 8, 9, 16, 17, 12, 9, 16, 19, 22, 31, 46, 41, 18, 3, 6, 7, 8, 9, 16, 17, 12, 9, 16, 19, 22, 31, 46, 41, 20, 9, 16, 19, 22, 31, 46, 43, 30, 31, 48
Offset: 1

Views

Author

Omar E. Pol, Dec 07 2009

Keywords

Comments

a(n) is the number of toothpicks added at the n-th round in the toothpick structure of A168112.

Examples

			If written as a triangle, begins:
1;
1;
2;
3,3;
3,6,7,6;
3,6,7,8,9,16,17,10;
3,6,7,8,9,16,17,12,9,16,19,22,31,46,41,18;
Rows converge to A168114.

Links

Crossrefs

Cf. A139250, A139251, A152978, A152980, A160407, A168112, A168114.

Formula

Observation: It appears that a(2^i+2) = 3, for i>0.
a(n) = A160731(n)/2. [From Nathaniel Johnston, Mar 28 2011]

Extensions

Terms after a(34) from Nathaniel Johnston, Mar 28 2011

A161413 First differences of A161412.

Original entry on oeis.org

1, 1, 1, 2, 4, 3, 3, 4, 6, 4, 5, 5, 10, 9, 5
Offset: 1

Views

Author

Omar E. Pol, Jun 10 2009

Keywords

Comments

Number of V-toothpicks added to the structure at the n-th round.

Links

Crossrefs

Cf. A139251, A160121, A160407, A161207, A161329, A161412.

A160718 a(n) = A160406(n+2)/2.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 15, 17, 20, 25, 29, 30, 31, 33, 35, 37, 40, 45, 49, 51, 54, 59, 64, 70, 80, 93, 101, 102, 103, 105, 107, 109, 112, 117, 121, 123, 126, 131, 136, 142, 152, 165, 173, 175, 178, 183, 188, 194, 204, 217, 226, 232, 242, 256, 271, 292
Offset: 0

Views

Author

Omar E. Pol, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A139250, A152998, A153000, A160406, A160407, A160719.

Formula

a(n) = A160719(n) + 1 = -a(n-1) + n + (A139250(n+1) + 5)/4 for n > 0. - Jinyuan Wang, Mar 04 2020

Extensions

More terms from Jinyuan Wang, Mar 04 2020

A160719 a(n) = A160406(n+2)/2 - 1.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 16, 19, 24, 28, 29, 30, 32, 34, 36, 39, 44, 48, 50, 53, 58, 63, 69, 79, 92, 100, 101, 102, 104, 106, 108, 111, 116, 120, 122, 125, 130, 135, 141, 151, 164, 172, 174, 177, 182, 187, 193, 203, 216, 225, 231, 241, 255, 270, 291
Offset: 0

Views

Author

Omar E. Pol, Jun 10 2009

Keywords

Links

Crossrefs

Cf. A139250, A153000, A160406, A160407, A160718.

Extensions

More terms from Jinyuan Wang, Mar 04 2020

A160729 First differences of A160728.

Original entry on oeis.org

6, 6, 12, 24, 24, 24, 24, 24, 48, 96, 96, 48, 24, 24, 48
Offset: 1

Views

Author

Omar E. Pol, Jul 28 2009

Keywords

Comments

Also, 6 times A160409.

Links

Crossrefs

Cf. A139250, A139251, A160161, A160407, A160409, A160728.

Formula

a(n) = A160409(n)*6.

A160419 a(n) = A160409(n+2)/2.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 4, 8
Offset: 1

Views

Author

Omar E. Pol, May 23 2009

Keywords

Links

Crossrefs

Cf. A139250, A139251, A160160, A160161, A160406, A160407, A160408, A160409, A160418.
Previous Showing 11-20 of 20 results.

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