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 1-3 of 3 results.

A163357 Hilbert curve in N X N grid, starting rightwards from the top-left corner, listed by descending antidiagonals.

Original entry on oeis.org

0, 1, 3, 14, 2, 4, 15, 13, 7, 5, 16, 12, 8, 6, 58, 19, 17, 11, 9, 57, 59, 20, 18, 30, 10, 54, 56, 60, 21, 23, 29, 31, 53, 55, 61, 63, 234, 22, 24, 28, 32, 52, 50, 62, 64, 235, 233, 25, 27, 35, 33, 51, 49, 67, 65, 236, 232, 230, 26, 36, 34, 46, 48, 68, 66, 78, 239, 237, 231
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Examples

			The top left 8 X 8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
   0  1 14 15 16 19 20 21
   3  2 13 12 17 18 23 22
   4  7  8 11 30 29 24 25
   5  6  9 10 31 28 27 26
  58 57 54 53 32 35 36 37
  59 56 55 52 33 34 39 38
  60 61 50 51 46 45 40 41
  63 62 49 48 47 44 43 42

Links

Crossrefs

Transpose: A163359. Inverse: A163358. One-based version: A163361. Row sums: A163365. Row 0: A163482. Column 0: A163483. Central diagonal: A062880. See also A163334 & A163336 for the Peano curve.
See also: A163540, A163542, A163547, A163898, A163899, A163900, A163538, A163539, A163904, A163907, A163917.

Programs

  • Mathematica
    b[{n_, k_}, {m_}] := (A[k, n] = m-1);
MapIndexed[b, List @@ HilbertCurve[4][[1]]];
Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)

Formula

a(n) = A163355(A054238(n)).

Extensions

Links to further derived sequences added by Antti Karttunen, Sep 21 2009

A163359 Hilbert curve in N x N grid, starting downwards from the top-left corner, listed by descending antidiagonals.

Original entry on oeis.org

0, 3, 1, 4, 2, 14, 5, 7, 13, 15, 58, 6, 8, 12, 16, 59, 57, 9, 11, 17, 19, 60, 56, 54, 10, 30, 18, 20, 63, 61, 55, 53, 31, 29, 23, 21, 64, 62, 50, 52, 32, 28, 24, 22, 234, 65, 67, 49, 51, 33, 35, 27, 25, 233, 235, 78, 66, 68, 48, 46, 34, 36, 26, 230, 232, 236, 79, 77, 71
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Examples

			The top left 8x8 corner of the array shows how this surjective self-avoiding walk begins (connect the terms in numerical order, 0-1-2-3-...):
   +0 +3 +4 +5 58 59 60 63
   +1 +2 +7 +6 57 56 61 62
   14 13 +8 +9 54 55 50 49
   15 12 11 10 53 52 51 48
   16 17 30 31 32 33 46 47
   19 18 29 28 35 34 45 44
   20 23 24 27 36 39 40 43
   21 22 25 26 37 38 41 42

Links

Crossrefs

Transpose: A163357, a(n) = A163357(A061579(n)). Inverse: A163360. One-based version: A163363. Row sums: A163365. Row 0: A163483. Column 0: A163482. Central diagonal: A062880.
See also A163334 and A163336 for the Peano curve.

Programs

  • Mathematica
    b[{n_, k_}, {m_}] := (A[n, k] = m-1);
MapIndexed[b, List @@ HilbertCurve[4][[1]]];
Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Mar 07 2021 *)

A163477 Row sums of A163357 and A163359 divided by 4.

Original entry on oeis.org

0, 1, 5, 10, 25, 43, 62, 84, 142, 205, 275, 350, 423, 503, 588, 680, 908, 1145, 1393, 1650, 1925, 2211, 2506, 2812, 3098, 3397, 3711, 4038, 4371, 4719, 5080, 5456, 6360, 7281, 8221, 9178, 10161, 11163, 12182, 13220, 14310, 15421, 16555, 17710
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Links

Crossrefs

Cf. A163357, A163359.

Programs

  • Mathematica
    nn = 8; s[{n_, k_}, {m_}] := (a[k, n] = m - 1); MapIndexed[s, List @@ HilbertCurve[nn][[1]]]; Floor[1/4*Map[Total, Table[a[n - k, k], {n, 0, nn^2}, {k, n, 0, -1}]]] (* Michael De Vlieger, Nov 01 2022, after Jean-François Alcover at A163357 *)

Formula

a(n) = floor(A163365(n)/4) (floor probably unnecessary).
Showing 1-3 of 3 results.

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