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Search: id:A129868
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| A129868 |
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Numbers palindromic in base 2: 0, 101, 11011, 1110111, 111101111,... |
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+0
2
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| 0, 5, 27, 119, 495, 2015, 8127, 32639, 130815, 523775, 2096127, 8386559, 33550335, 134209535, 536854527, 2147450879, 8589869055, 34359607295, 137438691327, 549755289599, 2199022206975, 8796090925055, 35184367894527
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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9+8a(n) = s^2 is a perfect square with s=2^(n+2)-1=3,7,15,31,63,...
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FORMULA
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a(n)=2*4^n-2^n-1=(2^n-1)*(2*2^n+1), n=0,1,...; G.f. = x(5 - 8*x)/(1 - 7*x + 14*x^2 - 8*x^3) recurrences: a(n)=(1/2)(7+8a(n-1)+sqrt(9+8a(n-1))), a(0)=0; a(n)=6*a(n-1)-8*a(n-2)-3, a(0)=0, a(1)=5; a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3), a(0)=0, a(1)=5, a(2)=27.
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MATHEMATICA
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(*1st*) FromDigits[ #, 2]&/@NestList[Append[Prepend[ #, 1], 1]&, {0}, 25] (*2nd*) NestList[(1/2)(7+8#+Sqrt[9+8# ])&, 0, 22]
f[n_] := 2^(2 n + 1) - 2^n - 1; Table[f@n, {n, 0, 22}] (* Robert G. Wilson v (rgwv@rgwv.com), Aug 24 2007 *)
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CROSSREFS
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Equals A006516(n+1)-1
Sequence in context: A064675 A135713 A085740 this_sequence A069993 A009027 A037498
Adjacent sequences: A129865 A129866 A129867 this_sequence A129869 A129870 A129871
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), May 24 2007
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