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.

A169757 First differences of A170907.

Original entry on oeis.org

3, 4, 5, 7, 8, 9, 10, 12, 14, 14, 14, 17, 19, 19, 20, 22, 25, 25, 23, 28, 29, 29, 29, 32, 36, 35, 33, 36, 40, 40, 40, 42, 46, 46, 46, 49, 49, 48, 44, 56, 57, 56, 51, 57, 61, 60, 59, 62, 68, 68, 62, 67, 71, 70, 68, 71, 78, 78, 73, 74, 80, 82, 81, 82, 87, 87, 93, 84, 96, 87, 88, 96, 100
Offset: 0

Views

Author

N. J. A. Sloane, May 06 2010

Keywords

Comments

a(314) = -59 is the first negative term.
I wish I had a recurrence for this sequence!

Links

Crossrefs

Cf. A170907, A169758.

A169758 Second differences of A170907.

Original entry on oeis.org

1, 1, 2, 1, 1, 1, 2, 2, 0, 0, 3, 2, 0, 1, 2, 3, 0, -2, 5, 1, 0, 0, 3, 4, -1, -2, 3, 4, 0, 0, 2, 4, 0, 0, 3, 0, -1, -4, 12, 1, -1, -5, 6, 4, -1, -1, 3, 6, 0, -6, 5, 4, -1, -2, 3, 7, 0, -5, 1, 6, 2, -1, 1, 5, 0, 6, -9, 12, -9, 1, 8, 4, -6, -8, 14, -11, 23, -41, 58, -19, 0, -7, 6, 3, -3, -7, 13, 6, -1, -10, 4, 8, 1, -3, 2, 8, 1, -2, 3, 0
Offset: 0

Views

Author

N. J. A. Sloane, May 06 2010

Keywords

Comments

I wish I had a recurrence for this sequence!

Crossrefs

Cf. A170907, A169757.

A163862 a(n) = A170907(2^n).

Original entry on oeis.org

1, 4, 13, 47, 176, 678, 2658, 10521, 41860, 166995, 667100, 2666651, 10663099, 42645332
Offset: 0

Views

Author

N. J. A. Sloane, May 11 2010

Keywords

Comments

This sequence determines the "lim sup" of the growth of A151723.

Crossrefs

Cf. A151723, A170907.

Formula

It appears that a(n)/4^n converges to a constant c which is roughly 0.635.

Extensions

a(8) onwards from David Applegate, May 12 2010

A170906 Triangle read by rows: T(n,k) = number of cells that are turned from OFF to ON at stage k of the cellular automaton in the 30-60-90 triangle of hexagons defined in Comments.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 4, 1, 2, 1, 1, 2, 2, 4, 2, 2, 3, 3, 1, 1, 2, 2, 4, 2, 4, 5, 4, 1, 2, 1, 1, 2, 2, 4, 2, 4, 6, 6, 1, 2, 3, 3, 1, 1, 2, 2, 4, 2, 4, 6, 8, 1, 2, 3, 5, 3, 3, 1, 1, 2, 2, 4, 2, 4, 6, 8, 2, 2, 3, 5, 5, 3, 5, 4, 1, 1, 2, 2, 4, 2, 4, 6, 8, 2, 4, 5, 6, 7, 6, 6, 4, 1, 2, 1
Offset: 1

Views

Author

N. J. A. Sloane, Jan 24 2010

Keywords

Comments

Consider the tiling of the plane by hexagons, where each cell has 6 neighbors, as in the A151723, A151724, A170905.
Assume the hexagons are oriented so that each one has a pair of vertical edges.
Consider the (30 deg., 60 deg., 90 deg.) triangle of hexagons with n hexagons along the short side, along the X-axis, 2n-1 hexagons along the hypotenuse and n hexagons separated by single edges along the middle side, along the Y-axis.
Initially all cells are OFF. At stage 1, the cell in the 60-degree corner is turned ON; thereafter, a cell is turned ON if it has exactly one ON neighbor in the triangle. Once a cell is ON it stays ON.
T(n,k) is the number of cells that are turned from OFF to ON at stage k (1 <= k <= 2n-1).
The rows converge to A170905. The rows sums give A170907.
Row n contains 2n-1 terms.
I wish I had a recurrence for this sequence!

Examples

			Triangle begins:
1
1 2 1
1 2 2 2 1
1 2 2 4 1 2 1
1 2 2 4 2 2 3 3 1
1 2 2 4 2 4 5 4 1 2 1
1 2 2 4 2 4 6 6 1 2 3 3 1
1 2 2 4 2 4 6 8 1 2 3 5 3 3 1
1 2 2 4 2 4 6 8 2 2 3 5 5 3 5 4 1
1 2 2 4 2 4 6 8 2 4 5 6 7 6 6 4 1 2 1
...
Row n = 4, [1 2 2 4 1 2 1], corresponds to the sequence of cells being turned ON shown in the following triangle (X denotes a cell that stays OFF). The hexagons have to be imagined.
7
.6
6.5
.X.4
X.4.3
.4.X.2
4.3.2.1

Links

Crossrefs

Cf. A151723, A151724, A170905, A170907, A169782 (partial sums across rows).
Showing 1-4 of 4 results.

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

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