

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
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



