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A160570
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Triangle read by rows, A160552 convolved with (1, 2, 2, 2,...); row sums = A139250, the Toothpick sequence.
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3
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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
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1,3
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LINKS
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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
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FORMULA
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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.
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EXAMPLE
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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. 4-th term in the Toothpick sequence.
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MAPLE
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T:=proc(n, k)if(k=1)then return A160552(n):else return 2*A160552(n-k+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
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CROSSREFS
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Cf. A160552, A139250
Sequence in context: A152197 A049342 A112966 * A128830 A090387 A030329
Adjacent sequences: A160567 A160568 A160569 * A160571 A160572 A160573
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson, May 19 2009
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STATUS
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approved
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