A170940 -id:A170940 - cp's OEIS frontend

A170929 When regarded as a triangle, the rows of A168131 converge to this sequence.

1, 4, 5, 3, 7, 17, 17, 7, 6, 13, 13, 13, 32, 55, 45, 15, 6, 13, 13, 13, 31, 51, 41, 20, 25, 39, 39, 58, 120, 159, 109, 31, 6, 13, 13, 13, 31, 51, 41, 20, 25, 39, 39, 58, 119, 155, 105, 36, 25, 39, 39, 57, 113, 143, 102, 65, 89, 117, 136, 236, 400, 431, 253, 63, 6, 13, 13, 13, 31

Offset: 0

N. J. A. Sloane, Feb 04 2010

nonn

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Sum_{i=0 .. 2^k - 1} a(i) = 4^i - 2^i - 2 for k >= 2 (cf. A170940).

A173521 a(n) is the concatenation of n 1's, 0, n 1's and 0.

Original entry on oeis.org

0, 1010, 110110, 11101110, 1111011110, 111110111110, 11111101111110, 1111111011111110, 111111110111111110, 11111111101111111110, 1111111111011111111110, 111111111110111111111110

Offset: 0

Omar E. Pol, Mar 16 2010

a(n) is also A170940(n+1) written in base 2.

			n ............... a(n)
0 ................ 0
1 ............... 1010
2 .............. 110110
3 ............. 11101110
4 ............ 1111011110
5 ........... 111110111110
6 .......... 11111101111110
7 ......... 1111111011111110
8 ........ 111111110111111110
9 ....... 11111111101111111110

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. A138148, A170940.

Table[FromDigits[Join[PadRight[{},n,1],{0},PadRight[{},n,1],{0}]],{n,0,20}] (* Harvey P. Dale, Feb 25 2012 *)

Vec(10*x*(200*x-101)/((x-1)*(10*x-1)*(100*x-1))  + O(x^100)) \\ Colin Barker, Sep 17 2013

G.f.: 10*x*(200*x-101) / ((x-1)*(10*x-1)*(100*x-1)). [Colin Barker, Sep 17 2013]

cp's OEIS Frontend

A170929 When regarded as a triangle, the rows of A168131 converge to this sequence.

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A173521 a(n) is the concatenation of n 1's, 0, n 1's and 0.

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