

A160570


Triangle read by rows, A160552 convolved with (1, 2, 2, 2,...); row sums = A139250, the Toothpick sequence.


3



1, 1, 2, 3, 2, 2, 1, 6, 2, 2, 3, 2, 6, 2, 2, 5, 6, 2, 6, 2, 2, 7, 10, 6, 2, 6, 2, 2, 1, 14, 10, 6, 2, 6, 2, 2, 3, 2, 14, 10, 6, 2, 6, 2, 2, 5, 6, 2, 14, 10, 6, 2, 6, 2, 2, 7, 10, 6, 2, 14, 10, 6, 2, 6, 2, 2, 5, 14, 10, 6, 2, 14, 10, 6, 2, 6, 2, 2, 11, 10, 14, 10, 6, 2, 14, 10, 6, 2, 6
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OFFSET

1,3


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

Construct triangle M = an infinite lower triangular Toeplitz matrix with A160552: (1, 1, 3, 1, 3, 5, 7,...) in every column. Let Q = an infinite lower triangular matrix with (1, 2, 2, 2, 2,...) as the main diagonal and the rest zeros. A160570 = M * Q.


EXAMPLE

First few rows of the triangle =
.1;
.1, 2;
.3, 2, 2;
.1, 6, 2, 2;
.3, 2, 6, 2, 2;
.5, 6, 2, 6, 2, 2;
.7, 10, 6, 2, 6, 2, 2;
.1, 14, 10, 6, 2, 6, 2, 2;
.3, 2, 14, 10, 6, 2, 6, 2, 2;
.5, 6, 2, 14, 10, 6, 2, 6, 2, 2;
....
Example: Row 4 = (1, 6, 2, 2) = (1, 3, 1, 1) dot (1, 2, 2, 2); where (1 + 6 + 2 + 2) = A139250(4), i.e., 4th term in the Toothpick sequence.


MAPLE

T:=proc(n, k)if(k=1)then return A160552(n):else return 2*A160552(nk+1):fi:end:
for n from 1 to 8 do for k from 1 to n do print(T(n, k)); od:od: # Nathaniel Johnston, Apr 13 2011


CROSSREFS

Cf. A160552, A139250.
Sequence in context: A049342 A112966 A286657 * A128830 A090387 A030329
Adjacent sequences: A160567 A160568 A160569 * A160571 A160572 A160573


KEYWORD

nonn,tabl,easy


AUTHOR

Gary W. Adamson, May 19 2009


STATUS

approved



