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A151685 a(n) = sum_{k >= 0} bin2(wt(n+k),k+1), where bin2(i,j) = A013609(i,j), wt(i) = A000120(i). 11
3, 7, 5, 7, 17, 17, 7, 7, 17, 17, 19, 41, 51, 31, 9, 7, 17, 17, 19, 41, 51, 31, 21, 41, 51, 55, 101, 143, 113, 49, 11, 7, 17, 17, 19, 41, 51, 31, 21, 41, 51, 55, 101, 143, 113, 49, 23, 41, 51, 55, 101, 143, 113, 73, 103, 143, 161, 257, 387, 369, 211, 71, 13, 7, 17, 17, 19, 41, 51 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Or, a(n) = sum_{k >= 0} 2^wt(k) * binomial(wt(n+k),k).

LINKS

Table of n, a(n) for n=0..68.

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

G.f.: Prod_{ k >= 0 } (1 + 2*x^(2^k-1) + x^(2^k)).

EXAMPLE

Contribution from Omar E. Pol, Jun 09 2009: (Start)

Triangle begins:

.3;

.7,5;

.7,17,17,7;

.7,17,17,19,41,51,31,9;

.7,17,17,19,41,51,31,21,41,51,55,101,143,113,49,11;

.7,17,17,19,41,51,31,21,41,51,55,101,143,113,49,23,41,51,55,101,143,113,...

(End)

MAPLE

bin2:=proc(n, k) option remember; if k<0 or k>n then 0

elif k=0 then 1 else 2*bin2(n-1, k-1)+bin2(n-1, k); fi; end;

wt := proc(n) local w, m, i;

w := 0; m := n; while m > 0 do i := m mod 2; w := w+i; m := (m-i)/2; od; w; end:

f:=n->add( bin2(wt(n+k), k), k=0..120 );

# or:

f := n->add( 2^k*binomial(wt(n+k), k), k=0..20 );

CROSSREFS

For generating functions of the form Prod_{k>=c} (1+a*x^(2^k-1)+b*x^2^k)) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694

Cf. A151689, A151691.

Cf. A000079. [From Omar E. Pol, Jun 09 2009]

Sequence in context: A287660 A122001 A161327 * A019809 A305741 A021270

Adjacent sequences:  A151682 A151683 A151684 * A151686 A151687 A151688

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 01 2009

STATUS

approved

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Last modified October 19 16:07 EDT 2018. Contains 316366 sequences. (Running on oeis4.)