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 A170838 G.f.: Product_{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 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 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: MATHEMATICA With[{nn=60}, CoefficientList[Series[Product[1+x^(2^k-1)+3x^2^k, {k, 0, nn}], {x, 0, nn}], x]] (* Harvey P. Dale, Dec 29 2021 *) CROSSREFS A170838-A170852, A170854-A170872 were added to supplement Gary W. Adamson's A162956. Sequence in context: A159073 A088343 A110781 * A115248 A005123 A332821 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 March 26 11:37 EDT 2023. Contains 361549 sequences. (Running on oeis4.)