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A151685
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a(n) = sum_{k >= 0} bin2(wt(n+k),k+1), where bin2(i,j) = A013609(i,j), wt(i) = A000120(i).
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11
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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; internal format)
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OFFSET
| 0,1
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COMMENTS
| Or, a(n) = sum_{k >= 0} 2^wt(k) * binomial(wt(n+k),k).
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LINKS
| 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
| G.f.: Prod_{ k >= 0 } (1 + 2*x^(2^k-1) + x^(2^k)).
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EXAMPLE
| Contribution from Omar E. Pol (info(AT)polprimos.com), 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)
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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 );
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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 (info(AT)polprimos.com), Jun 09 2009]
Sequence in context: A116535 A122001 A161327 * A019809 A021270 A113910
Adjacent sequences: A151682 A151683 A151684 * A151686 A151687 A151688
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 01 2009
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