A160570 Triangle read by rows, A160552 convolved with (1, 2, 2, 2, ...); row sums = A139250, the Toothpick sequence.

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

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), 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

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(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

Crossrefs

Cf. A160552, A139250.

Sequence in context: A112966 A286657 A334052 * A128830 A090387 A030329

Adjacent sequences: A160567 A160568 A160569 * A160571 A160572 A160573

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, May 19 2009

Status

approved