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.

A160428 Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160410, using cubes.

Original entry on oeis.org

0, 8, 64, 120, 512, 568, 960, 1352, 4096, 4152, 4544, 4936, 7680, 8072, 10816, 13560, 32768, 32824, 33216, 33608, 36352, 36744, 39488, 42232, 61440, 61832, 64576, 67320, 86528, 89272, 108480, 127688, 262144, 262200, 262592, 262984, 265728, 266120, 268864, 271608
Offset: 0

Views

Author

Omar E. Pol, Jun 01 2009

Keywords

Links

Crossrefs

Cf. A139250, A160119, 160379, A160410, A160429, A161340, A161342.

Programs

  • Mathematica
    a[n_] := 8*Sum[7^DigitCount[k, 2, 1], {k, 0, n - 1}]; Array[a, 40, 0] (* Michael De Vlieger, Nov 01 2022 *)

Formula

a(n) = 8 * Sum_{k=0..n-1} 7^A000120(k)
a(n) = 8 + 56 * Sum_{k=1..n-1} A151785(k) for n >= 1

Extensions

Formulas and more terms from Nathaniel Johnston, Nov 13 2010
More terms from Michael De Vlieger, Nov 01 2022

A161341 First differences of A161340.

Original entry on oeis.org

1, 26, 56, 260, 56, 392, 392, 2192, 56, 392, 392, 2744, 392, 2744, 2744, 16952, 56, 392, 392, 2744, 392, 2744, 2744, 19208, 392, 2744, 2744, 19208, 2744, 19208, 19208, 125336, 56, 392, 392, 2744, 392, 2744, 2744, 19208, 392, 2744, 2744, 19208, 2744, 19208, 19208
Offset: 1

Views

Author

Omar E. Pol, Jun 14 2009

Keywords

Examples

			From _Omar E. Pol_, Mar 15 2020: (Start)
Written as an irregular triangle in which row lengths give A011782 the sequence begins:
1;
26;
56, 260;
56, 392, 392, 2192;
56, 392, 392, 2744, 392, 2744, 2744, 16952;
56, 392, 392, 2744, 392, 2744, 2744, 19208, 392, 2744, 2744, 19208, 2744, ...
(End)

Crossrefs

Cf. A011782, A160414, A161340, A161415.

Programs

  • PARI
    f(n) = 8*7^hammingweight(n-1); \\ A160429
ispow2(n) = my(k); (n==2) || (ispower(n,,&k) && (k==2));
a(n) = if (n==1, 1, if (ispow2(n), f(n) - 3*n*(3*n - 1), f(n))); \\ Michel Marcus, Mar 15 2020

Formula

a(n) = A160429(n) for n>1 and n not a power of 2.
a(n) = A160429(n) - 3n*(3n - 1) for n>1 and n a power of 2.

Extensions

Formula and more terms from Nathaniel Johnston, Nov 15 2010
More terms from Jinyuan Wang, Mar 14 2020

A161343 a(n) = 7^A000120(n).

Original entry on oeis.org

1, 7, 7, 49, 7, 49, 49, 343, 7, 49, 49, 343, 49, 343, 343, 2401, 7, 49, 49, 343, 49, 343, 343, 2401, 49, 343, 343, 2401, 343, 2401, 2401, 16807, 7, 49, 49, 343, 49, 343, 343, 2401, 49, 343, 343, 2401, 343, 2401, 2401, 16807, 49, 343, 343, 2401, 343, 2401, 2401, 16807, 343, 2401, 2401, 16807, 2401, 16807, 16807, 117649
Offset: 0

Views

Author

Omar E. Pol, Jun 14 2009

Keywords

Comments

Also first differences of A161342.
From Omar E. Pol, May 03 2015: (Start)
It appears that when A151785 is regarded as a triangle in which the row lengths are the powers of 2, this is what the rows converge to.
Also this is also a row of the square array A256140.
(End)

Examples

			From _Omar E. Pol_, May 03 2015: (Start)
Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
7;
7, 49;
7, 49, 49, 343;
7, 49, 49, 343, 49, 343, 343, 2401;
7, 49, 49, 343, 49, 343, 343, 2401, 49, 343, 343, 2401, 343, 2401, 2401, 16807;
...
Row sums give A055274.
Right border gives A000420.
(End)

Links

Crossrefs

Cf. A000420, A011782, A055274, A160410, A151785, A161411, A160428, A160429, A161342, A256140, A256141.
Rows of the array A256140 are: A000007, A000012, A001316, A048883, A102376, A256135, A256136, this sequence.

Programs

  • PARI
    a(n) = 7^hammingweight(n); \\ Omar E. Pol, May 03 2015

Formula

a(n) = A000420(A000120(n)). - Omar E. Pol, May 03 2015
G.f.: Product_{k>=0} (1 + 7*x^(2^k)). - Ilya Gutkovskiy, Mar 02 2017

Extensions

More terms from Sean A. Irvine, Mar 08 2011
New name from Omar E. Pol, May 03 2015
a(52)-a(63) from Omar E. Pol, May 16 2015
Showing 1-3 of 3 results.

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