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.

Showing 1-4 of 4 results.

A316963 Same as A316668, except numbering of the squares starts at 0 rather than 1.

Original entry on oeis.org

0, 1, 2, 4, 3, 6, 7, 8, 5, 9, 13, 12, 11, 10, 15, 16, 17, 18, 19, 14, 20, 26, 25, 24, 23, 22, 21, 28, 29, 30, 31, 32, 33, 34, 27, 35, 43, 42, 41, 40, 39, 38, 37, 36, 45, 46, 47, 48, 49, 50, 51, 52, 53, 44, 54, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 66, 67
Offset: 0

Views

Author

Daniël Karssen, Jul 17 2018

Keywords

Comments

a(n) = A316668(n+1)-1.
See A316668 for further information.

Links

Crossrefs

Cf. A316668

A316671 Squares visited by moving diagonally one square on a diagonally numbered board and moving to the lowest available unvisited square at each step.

Original entry on oeis.org

1, 5, 4, 12, 11, 23, 22, 38, 37, 57, 56, 80, 79, 107, 106, 138, 137, 173, 172, 212, 211, 255, 254, 302, 301, 353, 352, 408, 407, 467, 466, 530, 529, 597, 596, 668, 667, 743, 742, 822, 821, 905, 904, 992, 991, 1083, 1082, 1178, 1177, 1277, 1276, 1380, 1379
Offset: 1

Views

Author

Daniël Karssen, Jul 15 2018

Keywords

Comments

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 .
.

Links

Crossrefs

Cf. A316588, A316668, A316669, A316670.

Programs

  • Mathematica
    CoefficientList[ Series[-(2x^4 - 3x^2 + 4x + 1)/((x - 1)^3 (x + 1)^2), {x, 0, 52}], x] (* or *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 5, 4, 12, 11}, 53] (* Robert G. Wilson v, Jul 18 2018 *)
  • PARI
    Vec(x*(1 + 4*x - 3*x^2 + 2*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^40)) \\ Colin Barker, Jul 18 2018

Formula

From Colin Barker, Jul 18 2018: (Start)
G.f.: x*(1 + 4*x - 3*x^2 + 2*x^4) / ((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>5.
a(n) = (n^2 + n + 4)/2 for n even.
a(n) = (n^2 - n + 2)/2 for n odd.
(End)

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

Views

Author

Daniël Karssen, Jul 15 2018

Keywords

Comments

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.

Links

Crossrefs

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

Views

Author

Daniël Karssen, Jul 15 2018

Keywords

Comments

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.

Links

Crossrefs

Cf. A316588, A316668, A316669, A316671.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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