Search: id:A052955 Results 1-1 of 1 results found. %I A052955 %S A052955 1,2,3,5,7,11,15,23,31,47,63,95,127,191,255,383,511,767,1023,1535,2047, %T A052955 3071,4095,6143,8191,12287,16383,24575,32767,49151,65535,98303,131071, %U A052955 196607,262143,393215,524287,786431,1048575,1572863,2097151,3145727 %N A052955 a(2n) = 2*2^n - 1, a(2n+1) = 3*2^n - 1. %C A052955 a(n) = least k such that A056792(k) = n. %C A052955 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] %H A052955 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1026 %F A052955 -1+Sum(1/4*(3+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z^2)) %F A052955 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 %F A052955 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. %F A052955 a(n) = 1 + partial sum of A016116(k-1). - Robert G. Wilson v Jun 05 2004 %F A052955 A132340(a(n)) = A027383(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007 %F A052955 a(n)=A027383(n-1)+1 for n>0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007 %F A052955 a(n)=A132666(a(n+1)-1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007 %F A052955 a(n)=A132666(a(n-1))+1 for n>0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007 %F A052955 A132666(a(n))=a(n+1)-1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007 %F A052955 a(n) = A027383(n+1)/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008 %F A052955 a(n) = 2*a(n-2) + 1 [From Richard Torres (richyrich12887(AT)yahoo.com), Apr 22 2009] %p A052955 spec := [S,{S=Prod(Sequence(Prod(Union(Z,Z),Z)),Union(Sequence(Z),Z))}, unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20); %p A052955 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 %p A052955 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 %t A052955 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) %t A052955 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] %Y A052955 Cf. A000225 for even terms, A055010 for odd terms. See also A056792. %Y A052955 Essentially 1 more than A027383, 2 more than A060482. [Comment corrected by Klaus Brockhaus, Aug 09 2009] %Y A052955 Union of A000225 & A055010. %Y A052955 For partial sums see A027383. %Y A052955 Cf. A132666. %Y A052955 Sequence in context: A116601 A024792 A055771 this_sequence A165801 A022480 A024791 %Y A052955 Adjacent sequences: A052952 A052953 A052954 this_sequence A052956 A052957 A052958 %K A052955 easy,nonn %O A052955 0,2 %A A052955 encyclopedia(AT)pommard.inria.fr, Jan 25 2000 %E A052955 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. Search completed in 0.002 seconds