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.

A256139 First differences of A256138.

Original entry on oeis.org

1, 4, 4, 12, 4, 12, 20, 28, 4, 12, 20, 36, 36, 28, 52, 60, 4, 12, 20, 36, 36, 36, 68, 100, 68, 28, 52, 92, 108, 76, 124, 124, 4, 12, 20, 36, 36, 36, 68, 100, 68, 36, 68, 116, 148, 132, 164, 228, 132, 28, 52, 92, 108, 108, 172, 268, 236, 108, 124, 220, 276, 196, 276, 252
Offset: 0

Views

Author

Omar E. Pol, Mar 20 2015

Keywords

Comments

Number of cells turned ON at n-th stage in the structure of A256138.
First differs from A169708 at a(11).

Examples

			Written as an irregular triangle in which the row lengths are the terms of A011782 the sequence begins:
1;
4;
4,12;
4,12,20,28;
4,12,20,36,36,28,52,60;
4,12,20,36,36,36,68,100,68,28,52,92,108,76,124,124;
4,12,20,36,36,36,68,100,68,36,68,116,148,132,164,228,132,28,52,92,108,108,172,268,236,108,124,220,276,196,276,252;
...
It appears that the right border gives A173033.

Links

Crossrefs

Cf. A028399, A011782, A151723, A151724, A160721, A169708, A170898, A170905, A173033, A256138.

Formula

a(n) = 2*A151724(n+1)/3, n >= 1.

A256250 Total number of ON states after n generations of a cellular automaton on the square grid.

Original entry on oeis.org

1, 5, 9, 21, 25, 37, 57, 85, 89, 101, 121, 149, 185, 229, 281, 341, 345, 357, 377, 405, 441, 485, 537, 597, 665, 741, 825, 917, 1017, 1125, 1241, 1365, 1369, 1381, 1401, 1429, 1465, 1509, 1561, 1621, 1689, 1765, 1849, 1941, 2041, 2149, 2265, 2389, 2521, 2661, 2809, 2965, 3129, 3301, 3481, 3669, 3865, 4069, 4281, 4501, 4729, 4965, 5209, 5461
Offset: 1

Views

Author

Omar E. Pol, Mar 20 2015

Keywords

Comments

A256251 gives the number of cells turned ON at n-th stage.
Note that the number of cells turned ON at n-th stage in each one of its four quadrants is also A006257 (Josephus problem). For more information see A256249.
It appears that this is also a bisection of A256249.
First differs from A169707 at a(13), but both sequences share infinitely many terms. This one is simpler. Compare A169707.

Examples

			Also, written as an irregular triangle T(n,k), k >= 1, in which the row lengths are the terms of A011782 the sequence begins:
1;
5;
9,   21;
25,  37, 57, 85;
89, 101,121,149,185,229,281,341;
345,357,377,405,441,485,537,597,665,741,825,917,1017,1125,1241,1365;
...
Right border gives the positive terms of A002450.
It appears that this triangle at least shares with the triangles from the following sequences; A147562, A162795, A169707, A255366, the positive elements of the columns k, if k is a power of 2.

Links

Crossrefs

Cf. A002450, A006257, A011782, A139250, A147562, A160720, A162795, A169707, A246335, A255366, A256138, A256249, A256251.

Programs

Formula

a(n) = 1 + 4*A256249(n-1), n >= 1.

A256536 Corner sequence associated with A151723.

Original entry on oeis.org

1, 4, 9, 18, 27, 36, 53, 78, 95, 104, 121, 150, 187, 220, 261, 318, 351, 360, 377, 406, 443, 480, 533, 618, 703, 752, 793, 866, 967, 1060, 1161, 1286, 1351, 1360, 1377, 1406, 1443, 1480, 1533, 1618, 1703, 1756, 1809, 1902, 2035, 2176, 2325, 2522, 2703, 2784, 2825, 2898, 2999, 3108, 3249, 3470, 3723, 3896, 4013, 4186, 4435, 4672, 4909, 5174, 5303
Offset: 1

Views

Author

Omar E. Pol, Apr 01 2015

Keywords

Comments

Total number of ON cells after n generations in one of the outside corners of an infinite hexagon-shaped structure on hexagonal grid.
For an animation see "The movie version" in Links section.
Partial sums of A256537.
See also the Formula section in A256537.
Compare A256138.

Links

Crossrefs

Cf. A151723, A153006, A169779, A256138, A256537.
Showing 1-3 of 3 results.

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

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