A316671 -id:A316671 - cp's OEIS frontend

A316966 Same as A316671, except numbering of the squares starts at 0 rather than 1.

0, 4, 3, 11, 10, 22, 21, 37, 36, 56, 55, 79, 78, 106, 105, 137, 136, 172, 171, 211, 210, 254, 253, 301, 300, 352, 351, 407, 406, 466, 465, 529, 528, 596, 595, 667, 666, 742, 741, 821, 820, 904, 903, 991, 990, 1082, 1081, 1177, 1176, 1276, 1275, 1379, 1378

Offset: 0

Daniël Karssen, Jul 17 2018

See A316671 for further information.

Daniël Karssen, Table of n, a(n) for n = 0..9999
Daniël Karssen, Figure showing the first 6 steps of the sequence
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A316671.

Cf. A128918: it is provided by a(-n-1).

Table[1 + (n + 2) (n - (-1)^n)/2, {n, 0, 60}] (* Bruno Berselli, Jul 19 2018 *)

concat(0, Vec(x*(4 - x + x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Jul 19 2018

a(n) = A316671(n+1) - 1.
From Colin Barker, Jul 19 2018: (Start)
G.f.: x*(4 - x + x^3) / ((1 - x)^3*(1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. (End)
a(n) = 1 + (n + 2)*(n - (-1)^n)/2. - Bruno Berselli, Jul 19 2018

A316884 Squares visited by moving diagonally one square on a spirally numbered board and moving to the lowest available unvisited square at each step.

Original entry on oeis.org

1, 3, 11, 9, 23, 7, 19, 5, 15, 33, 13, 29, 53, 27, 25, 47, 77, 45, 21, 41, 69, 39, 17, 35, 61, 95, 59, 31, 55, 87, 127, 85, 51, 49, 79, 117, 163, 115, 75, 43, 71, 107, 151, 105, 67, 37, 63, 97, 139, 189, 137, 93, 57, 89, 129, 177, 233, 175, 125, 83, 81, 119

Offset: 1

Daniël Karssen, Jul 15 2018

nonn

Board is numbered with the square spiral:
.
  17--16--15--14--13
   |               |
  18   5---4---3  12   .
   |   |       |   |
  19   6   1---2  11   .
   |   |           |
  20   7---8---9--10   .
   |
  21--22--23--24--25--26

Daniël Karssen, Table of n, a(n) for n = 1..10000
Daniël Karssen, Figure showing the first 49 steps of the sequence

Cf. A316667, A316671.

A316668 Squares visited by king moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 8, 9, 6, 10, 14, 13, 12, 11, 16, 17, 18, 19, 20, 15, 21, 27, 26, 25, 24, 23, 22, 29, 30, 31, 32, 33, 34, 35, 28, 36, 44, 43, 42, 41, 40, 39, 38, 37, 46, 47, 48, 49, 50, 51, 52, 53, 54, 45, 55, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 67, 68

Offset: 1

Daniël Karssen, Jul 15 2018

nonn

Board is numbered as follows:
   1  2  4  7 11 16  .
   3  5  8 12 17  .
   6  9 13 18  .
  10 14 19  .
  15 20  .
  21  .
   .
Same as A316588 but with king move instead of knight move.

Daniël Karssen, Table of n, a(n) for n = 1..100000
Daniël Karssen, Figure showing the first 26 steps of the sequence

Cf. A316588, A316669, A316670, A316671.

A316669 Squares visited by queen moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.

Original entry on oeis.org

1, 2, 3, 5, 4, 6, 9, 7, 8, 10, 14, 11, 12, 13, 15, 20, 16, 17, 18, 19, 21, 27, 22, 23, 24, 25, 26, 28, 35, 29, 30, 31, 32, 33, 34, 36, 44, 37, 38, 39, 40, 41, 42, 43, 45, 54, 46, 47, 48, 49, 50, 51, 52, 53, 55, 65, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 77

Offset: 1

Daniël Karssen, Jul 15 2018

nonn

Board is numbered as follows:
   1  2  4  7 11 16  .
   3  5  8 12 17  .
   6  9 13 18  .
  10 14 19  .
  15 20  .
  21  .
   .
Same as A316588 but with queen move instead of knight move.

Daniël Karssen, Table of n, a(n) for n = 1..10000
Daniël Karssen, Figure showing the first 22 steps of the sequence

Cf. A316588, A316668, A316670, A316671.

A316670 Squares visited by bishop moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.

Original entry on oeis.org

1, 5, 4, 6, 14, 11, 12, 13, 15, 27, 22, 23, 24, 25, 26, 28, 44, 37, 38, 39, 40, 41, 42, 43, 45, 65, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 90, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 119, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117

Offset: 1

Daniël Karssen, Jul 15 2018

nonn

Board is numbered as follows:
   1  2  4  7 11 16  .
   3  5  8 12 17  .
   6  9 13 18  .
  10 14 19  .
  15 20  .
  21  .
   .
Same as A316588 but with bishop move instead of knight move.

Daniël Karssen, Table of n, a(n) for n = 1..10000
Daniël Karssen, Figure showing the first 10 steps of the sequence

Cf. A316588, A316668, A316669, A316671.

cp's OEIS Frontend

A316966 Same as A316671, except numbering of the squares starts at 0 rather than 1.

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A316884 Squares visited by moving diagonally one square on a spirally numbered board and moving to the lowest available unvisited square at each step.

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A316668 Squares visited by king moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.

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A316669 Squares visited by queen moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.

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Author

Keywords

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Links

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A316670 Squares visited by bishop moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.

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Author

Keywords

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