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A033922
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Base 2 digital convolution sequence.
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1
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1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Definition: a(0) = 1; for n > 0, let the base 2 representation of n be 2^k_1 + ... + 2^k_i, then a(n) = a(k_1) + ... + a(k_i).
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..10000
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EXAMPLE
| For example, 6 = 2^2 + 2^1, so a(6) = a(2) + a(1) = 2.
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MAPLE
| a:= proc(n) option remember; local c, m, t; if n=0 then 1 else m:= n; c:=0; for t from 0 while m<>0 do c:= c+ `if` (irem (m, 2, 'm')=1, a(t), 0) od; c fi end: seq (a(n), n=0..120); # Alois P. Heinz, Jul 13 2011
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PROG
| (PARI) al(n)=local(v, k, e); v=vector(n+1); v[1]=1; for(m=1, n, k=m; e=0; while(k>0, if(k%2, v[m+1]+=v[e+1]); e++; k\=2)); v
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CROSSREFS
| Cf. A033639, A014221 (n such that a(n)=1).
Sequence in context: A143966 A178695 A029363 * A008624 A059169 A026922
Adjacent sequences: A033919 A033920 A033921 * A033923 A033924 A033925
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KEYWORD
| nonn,base
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AUTHOR
| Dave Wilson
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EXTENSIONS
| Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jul 13 2011
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