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.

A160798 a(n) = A160797(n+2)/3.

Original entry on oeis.org

1, 7, 1, 7, 3, 21, 1, 7, 3, 21, 3, 21, 9, 63, 1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189, 1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189, 3, 21, 9, 63, 9, 63, 27, 189, 9, 63, 27, 189, 27, 189, 81, 567, 1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63
Offset: 1

Views

Author

Omar E. Pol, Jun 13 2009

Keywords

Comments

From Omar E. Pol, Mar 15 2020: (Start)
It appears that the right border of triangle gives A005032.
It appears that the sum of n-th row equals A004171(n). (End)
Apparently A160417 shifted once left. - R. J. Mathar, May 30 2025

Examples

			From _Omar E. Pol_, Mar 15 2020: (Start)
Written as an irregular triangle in which row lengths are the even powers of 2, the sequence begins:
1, 7;
1, 7, 3, 21;
1, 7, 3, 21, 3, 21, 9, 63;
1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189;
1, 7, 3, 21, 3, 21, 9, 63, 3, 21, 9, 63, 9, 63, 27, 189, 3, 21, 9, 63, 9, 63, ...
(End)

Crossrefs

Cf. A004171, A005032, A160796, A160797.

Extensions

More terms from Jinyuan Wang, Mar 15 2020

A160796 Total number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton which is the "corner" structure corresponding to A160118.

Original entry on oeis.org

0, 1, 8, 11, 32, 35, 56, 65, 128, 131, 152, 161, 224, 233, 296, 323, 512, 515, 536, 545, 608, 617, 680, 707, 896, 905, 968, 995, 1184, 1211, 1400, 1481, 2048, 2051, 2072, 2081, 2144, 2153, 2216, 2243, 2432, 2441, 2504, 2531, 2720, 2747, 2936, 3017, 3584, 3593, 3656
Offset: 0

Views

Author

Omar E. Pol, Jun 13 2009, Jun 14 2009

Keywords

Comments

This bears the same relationship to A160118 as A153006 does to A139250.

Examples

			If we label the generations of cells turned ON by consecutive numbers we get the cell pattern shown below:
..9...............9
...888.888.888.888.
...878.878.878.878.
...8866688.8866688.
.....656.....656...
...8866444.4446688.
...878.434.434.878.
...888.4422244.888.
.........212.......
00000000002244.888.
0000000000.434.878.
0000000000.4446688.
0000000000...656...
0000000000.8866688.
0000000000.878.878.
0000000000.888.888.
0000000000........9
0000000000.........
0000000000.........

Crossrefs

Cf. A139250, A153006, A160797, A160798, A160412, A160118, A160416.

Programs

  • Mathematica
    With[{d = 2}, wt[n_] := DigitCount[n, 2, 1]; a[n_] := (5 + 3 * If[OddQ[n], 3^d + (2^d)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, (n - 1)/2}] + (2^d)*(3^d - 2)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, (n - 3)/2}], 3^d + (2^d)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, n/2 - 1}] + (2^d)*(3^d - 2)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, n/2 - 1}]]) / 4; a[0] = 0; a[1] = 1; Array[a, 50, 0]] (* Amiram Eldar, Aug 01 2023 *)

Formula

a(n) = 2 + (3/4)*(A160118(n) - 1) if n >= 2.

Extensions

Entry revised by Omar E. Pol and N. J. A. Sloane, Feb 16 2010
More terms from Nathaniel Johnston, Nov 13 2010
Corrected by Sean A. Irvine, Mar 23 2011, in response to correction to A160118
More terms from Amiram Eldar, Aug 01 2023

A162349 First differences of A160412.

Original entry on oeis.org

3, 9, 9, 27, 9, 27, 27, 81, 9, 27, 27, 81, 27, 81, 81, 243, 9, 27, 27, 81, 27, 81, 81, 243, 27, 81, 81, 243, 81, 243, 243, 729, 9, 27, 27, 81, 27, 81, 81, 243, 27, 81, 81, 243, 81, 243, 243, 729, 27, 81, 81, 243, 81, 243, 243, 729, 81, 243, 243, 729, 243, 729
Offset: 1

Views

Author

Omar E. Pol, Jul 14 2009

Keywords

Comments

Note that if A048883 is written as a triangle then rows converge to this sequence. - Omar E. Pol, Nov 15 2009

Links

Crossrefs

Cf. A063787, A152980, A160410, A160411, A160412, A160414, A160415, A160417, A160797.
Cf. A048883, A161415. - Omar E. Pol, Nov 15 2009

Programs

  • Mathematica
    a[n_] := 3^(1 + DigitCount[n - 1, 2, 1]); Array[a, 100] (* Amiram Eldar, Feb 02 2024 *)

Formula

a(n) = 3^A063787(n) = 3 * A048883(n-1). - Amiram Eldar, Feb 02 2024

Extensions

More terms from Omar E. Pol, Nov 15 2009
More terms from Colin Barker, Apr 19 2015
More terms from Amiram Eldar, Feb 02 2024

A161417 First differences of A160416.

Original entry on oeis.org

1, 7, 3, 21, 7, 41, 9, 57, 13
Offset: 1

Views

Author

Omar E. Pol, May 20 2009, Jun 14 2009

Keywords

Links

Crossrefs

Cf. A139250, A139251, A153006, A152980, A160411, A160413, A160415, A160416.
Cf. A160797.
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.