A134201 -id:A134201 - cp's OEIS frontend

A323647 Number of elements added at n-th stage to the toothpick structure of A323646.

1, 2, 2, 4, 6, 6, 6, 12, 14, 12, 6, 12, 14, 16, 18, 32, 34, 20, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 36, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92, 82, 40, 18, 32, 38, 44, 62, 92, 86, 60, 62, 96, 114, 144, 210, 260, 194, 68, 6, 12, 14, 16, 18, 32, 34, 24, 18, 32, 38, 44, 62, 92

Offset: 1

Omar E. Pol, Mar 07 2019

The "word" of this cellular automaton is "ab", but note that this triangle has an unusual structure: an additional row of length 2. For more information about the word of cellular automata see A296612.
The structure of the irregular triangle is as shown below:
a,b;
a,b;
a,b;
a,b,a,b;
a,b,a,b,a,b,a,b;
a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
...
Row lengths give 2 together with the terms of A011782 multiplied by 2, also 2 togheter with the column 2 of A296612.
Columns "a" contain numbers of toothpicks of length 2.
Columns "b" contain numbers of D-toothpicks of length 2*sqrt(2). See the example.

			Triangle begins:
1, 2;
2, 4;
6, 6;
6,12,14,12;
6,12,14,16,18,32,34,20;
6,12,14,16,18,32,34,24,18,32,38,44,62,92,82,36;
6,12,14,16,18,32,34,24,18,32,38,44,62,92,82,40,18,32,38,44,62,92,86,60,62,96, ...

First differences of A323646.
Also, 1 together with A160731.
Column 1 gives A134201.
Cf. A011782, A139251, A296612.
For other hybrid cellular automata, see A194271, A194701, A220501, A289841, A290221, A294021, A294963, A294981, A299771, A323651, A327331, A327333.

A278481 Number of neighbors of the n-th term in a full isosceles triangle read by rows.

Original entry on oeis.org

2, 4, 4, 4, 6, 4, 4, 6, 6, 4, 4, 6, 6, 6, 4, 4, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4

Offset: 1

Omar E. Pol, Nov 23 2016

Apart from the left border and the right border, the rest of the elements are 6's.

For the same idea but for a right triangle see A278480; for a square array see A278545, for a square spiral see A010731; and for a hexagonal spiral see A010722.

			The sequence written as an isosceles triangle begins:
.
.                     2;
.                   4,  4;
.                 4,  6,  4;
.               4,  6,  6,  4;
.             4,  6,  6,  6,  4;
.           4,  6,  6,  6,  6,  4;
.         4,  6,  6,  6,  6,  6,  4;
.       4,  6,  6,  6,  6,  6,  6,  4;
.     4,  6,  6,  6,  6,  6,  6,  6,  4;
.   4,  6,  6,  6,  6,  6,  6,  6,  6,  4;
...

Row sums give A016933.
Left border gives A040002, the same as the right border.
Middle column gives the elements > 1 of A134201, also twice A122553.
Cf. A010722, A010731, A275015, A278317, A278480, A278545.

A134202 Number of rigid Hv-groups of order n.

Original entry on oeis.org

1, 5, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14

Offset: 1

Roman Bayon (roman.bayon(AT)gmail.com), Oct 14 2007

nonn

R. Bayon and N. Lygeros, Hyperstructures and Automorphism Groups, submitted.
Th. Vougiouklis, The fundamental relation in hyperrings: The general hyperfield, Fourth Int. Congress Algebraic Hyperstructures and Appl. (AHA), 1991, pp. 203-211.

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A108089, A132590, A134201.

PadRight[{1,5,13},120,{14}] (* Harvey P. Dale, Aug 22 2019 *)

a(1)=1, a(2)=5, a(3)=13, a(n)=14 for n>3.

G.f.: -x*(1+4*x+8*x^2+x^3)/(-1+x). - R. J. Mathar, Nov 14 2007

cp's OEIS Frontend

A323647 Number of elements added at n-th stage to the toothpick structure of A323646.

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A278481 Number of neighbors of the n-th term in a full isosceles triangle read by rows.

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A134202 Number of rigid Hv-groups of order n.

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