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Search: id:A052955
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| A052955 |
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a(2n) = 2*2^n - 1, a(2n+1) = 3*2^n - 1. |
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+0
12
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| 1, 2, 3, 5, 7, 11, 15, 23, 31, 47, 63, 95, 127, 191, 255, 383, 511, 767, 1023, 1535, 2047, 3071, 4095, 6143, 8191, 12287, 16383, 24575, 32767, 49151, 65535, 98303, 131071, 196607, 262143, 393215, 524287, 786431, 1048575, 1572863, 2097151, 3145727
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = least k such that A056792(k) = n.
One quarter of the number of positive integer (n+2) X (n+2) arrays with every 2 X 2 subblock summing to 1. [From Ron Hardin (rhhardin(AT)att.net), Sep 29 2008]
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1026
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FORMULA
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-1+Sum(1/4*(3+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z^2))
a(n)=2^(n/2)(3sqrt(2)/4+1-(3sqrt(2)/4-1)(-1)^n)-1. - Paul Barry (pbarry(AT)wit.ie), May 23 2004
G.f.: (1 + x - x^2)/((1 - x)*(1 - 2*x^2)). a(0) = 1, a(1) = 2, a(n+2) = 2*a(n) + 1.
a(n) = 1 + partial sum of A016116(k-1). - Robert G. Wilson v Jun 05 2004
A132340(a(n)) = A027383(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007
a(n)=A027383(n-1)+1 for n>0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
a(n)=A132666(a(n+1)-1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
a(n)=A132666(a(n-1))+1 for n>0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
A132666(a(n))=a(n+1)-1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
a(n) = A027383(n+1)/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
a(n) = 2*a(n-2) + 1 [From Richard Torres (richyrich12887(AT)yahoo.com), Apr 22 2009]
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MAPLE
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spec := [S, {S=Prod(Sequence(Prod(Union(Z, Z), Z)), Union(Sequence(Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=2*a[n-2]+2 od: seq(a[n]/2, n=2..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-2]+2 od: seq(a[n]+1, n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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MATHEMATICA
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f[n_] := If[EvenQ[n], 2^(n/2 + 1) - 1, 3*2^((n - 1)/2) - 1]; Table[ f[n], {n, 0, 41}] (from Robert G. Wilson v Jun 05 2004)
Clear[a, b, c, m, n]; a[m_] := Table[If[IntegerDigits[n, 2] == Reverse[IntegerDigits[n, 2]], IntegerDigits[n, 2], {0}], {n, 0, 2^m}]; b[m_] := Union[Sort[a[m]]]; c[m_] := Table[FromDigits[b[m][[n]], 2], {n, 1, Length[b[m]]}]; Table[Length[c[m]], {m, 1, 12}] [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 06 2008]
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CROSSREFS
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Cf. A000225 for even terms, A055010 for odd terms. See also A056792.
Essentially 1 more than A027383, 2 more than A060482. [Comment corrected by Klaus Brockhaus, Aug 09 2009]
Union of A000225 & A055010.
For partial sums see A027383.
Cf. A132666.
Sequence in context: A116601 A024792 A055771 this_sequence A165801 A022480 A024791
Adjacent sequences: A052952 A052953 A052954 this_sequence A052956 A052957 A052958
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), May 03 2000. Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 29 2001.
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