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A170838 G.f.: Prod_{k >= 0} (1 + x^(2^k-1) + 3x^(2^k)). 2
2, 5, 9, 11, 11, 24, 36, 29, 11, 24, 38, 44, 57, 108, 135, 83, 11, 24, 38, 44, 57, 108, 137, 98, 57, 110, 158, 189, 279, 459, 486, 245, 11, 24, 38, 44, 57, 108, 137, 98, 57, 110, 158, 189, 279, 459, 488, 260, 57, 110, 158, 189, 279, 461, 509, 351, 281, 488, 663, 846, 1296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..60.

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

MAPLE

Maple program for A170838-A170852, A162956, A170854-A170872.

read format;

G := proc(a, b, c); mul( 1 + a*x^(2^n-1) + b*x^(2^n), n=c..20); end;

f := proc(a, b, c) seriestolist(series(G(a, b, c), x, 120)); end;

at:=170838:

for a from 1 to 2 do for c from 0 to 2 do

b:=3;

t1:=f(a, b, c);

lprint( format(t1, at) );

lprint("G.f.: Prod_{k >= ", c, "} (1 +", a, "* x^(2^k-1) +", b, "* x^(2^k)).");

at:=at+1; od: od:

for b from 1 to 3 do for c from 0 to 2 do

a:=3;

t1:=f(a, b, c);

lprint( format(t1, at) );

lprint("G.f.: Prod_{k >= ", c, "} (1 +", a, "* x^(2^k-1) +", b, "* x^(2^k)).");

at:=at+1; od: od:

h:=proc(r, s, a, b) local s1, n, i, j;

s1:=array(0..120);

s1[0]:=r; s1[1]:=s;

for n from 2 to 120 do i:=floor(log(n)/log(2));

j:=n-2^i; s1[n]:=a*s1[j]+b*s1[j+1]; od:

[seq(s1[n], n=0..120)];

end;

l1:=[[0, 1], [1, 0], [1, 1], [1, 2]];

l2:=[[3, 1], [3, 2], [1, 3], [2, 3], [3, 3]];

for i from 1 to 4 do for j from 1 to 5 do

r:=l1[i][1];

s:=l1[i][2];

a:=l2[j][1];

b:=l2[j][2];

t1:=h(r, s, a, b);

lprint(format(t1, at)); at:=at+1;

lprint("a(0)=", r, ", a(1)=", s, "; a(2^i+j)=", a, "*a(j)+", b, "a(j+1) for 0 <= j < 2^i.");

od: od:

CROSSREFS

A170838-A170852, A170854-A170872 were added to supplement Gary W. Adamson's A162956.

Sequence in context: A159073 A088343 A110781 * A115248 A005123 A283481

Adjacent sequences:  A170835 A170836 A170837 * A170839 A170840 A170841

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 02 2010

STATUS

approved

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Last modified February 20 02:07 EST 2018. Contains 299357 sequences. (Running on oeis4.)