A171166 -id:A171166 - cp's OEIS frontend

A171178 Permutation of the natural numbers: 0 together with the partial sums of A171177.

0, 2, 1, 6, 3, 5, 4, 12, 7, 11, 8, 10, 9, 20, 13, 19, 14, 18, 15, 17, 16, 30, 21, 29, 22, 28, 23, 27, 24, 26, 25, 42, 31, 41, 32, 40, 33, 39, 34, 38, 35, 37, 36, 56, 43, 55, 44, 54, 45, 53, 46, 52, 47, 51, 48, 50, 49, 72, 57, 71, 58, 70, 59, 69, 60, 68

Offset: 0

Omar E. Pol, Feb 23 2010

a(n) is also the value of "x" and "y" of the n-th point (x,y), located on the infinite straight line (0,0),(1,1)..., that is intercepted by the path in structure of A171166.

For another version see A171175.

Index entries for sequences that are permutations of the natural numbers

Cf. A000027, A005132, A171164, A161165, A161166, A171172, A171173, A171174, A171175, A171176, A171178, A172310.

A171176 Triangle read by rows in which row n lists 3n-1 together with the first 2n-1 positive integers, in reverse order.

Original entry on oeis.org

2, 1, 5, 3, 2, 1, 8, 5, 4, 3, 2, 1, 11, 7, 6, 5, 4, 3, 2, 1, 14, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Omar E. Pol, Feb 23 2010

a(n) is also the length of the n-th L-toothpick added to the structure of A171166.

			Triangle begins:
   2,  1;
   5,  3,  2,  1;
   8,  5,  4,  3,  2,  1;
  11,  7,  6,  5,  4,  3,  2,  1;
  14,  9,  8,  7,  6,  5,  4,  3,  2, 1;
  17, 11, 10,  9,  8,  7,  6,  5,  4, 3, 2, 1;
  20, 13, 12, 11, 10,  9,  8,  7,  6, 5, 4, 3, 2, 1;
  23, 15, 14, 13, 12, 11, 10,  9,  8, 7, 6, 5, 4, 3, 2, 1;
  26, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1;

Harvey P. Dale, Table of n, a(n) for n = 1..1000
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences

Cf. A000027, A016789, A172310, A171164, A161165, A161166, A171172, A171173, A171174, A171175, A171177, A171178.

Cf. A132209 (row sums). - R. J. Mathar, Mar 01 2010

Table[{3n-1,Reverse[Range[2n-1]]},{n,10}]//Flatten (* Harvey P. Dale, Jun 26 2022 *)

A171164 A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.

Original entry on oeis.org

0, 1, 2, 3, 4, 8, 12, 13, 14, 16, 18, 21, 24, 31, 38, 39, 40, 42, 44, 47, 50, 54, 58, 63, 68, 78, 88, 89, 90, 92, 94, 97, 100, 104, 108, 113, 118, 124, 130, 137, 144, 157, 170, 171, 172, 174, 176, 179, 182, 186, 190, 195, 200, 206, 212

Offset: 0

Omar E. Pol, Mar 14 2010

Note that the vertex 0 and the vertex 4 both are overlapping.
For other versions see A171165 and A171166.
Also, partial sums of the sequence formed by 0 together with the numbers of A171172 repeated.

Cf. A171165, A171166, A171172, A171173, A171174, A171175, A171176, A171177, A171178.

A171165 A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.

Original entry on oeis.org

0, 2, 4, 5, 6, 10, 14, 15, 16, 18, 20, 23, 26, 33, 40, 41, 42, 44, 46, 49, 52, 56, 60, 65, 70, 80, 90, 91, 92, 94, 96, 99, 102, 106, 110, 115, 120, 126, 132, 139, 146, 159, 172, 173, 174, 176, 178, 181, 184, 188, 192, 197, 202, 208, 214

Offset: 0

Omar E. Pol, Mar 14 2010

Also, partial sums of the sequence formed by 0 together the numbers of A171173 repeated.

For another version see A171166.

Cf. A171166, A171173, A171174, A171175, A171176, A171177, A171178.

cp's OEIS Frontend

A171178 Permutation of the natural numbers: 0 together with the partial sums of A171177.

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A171176 Triangle read by rows in which row n lists 3n-1 together with the first 2n-1 positive integers, in reverse order.

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A171164 A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.

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A171165 A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.

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Author

Keywords

Comments

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