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Search: id:A097110
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| A097110 |
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Expansion of (1+2x-2x^3)/(1-3x^2+2x^4). |
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+0
2
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| 1, 2, 3, 4, 7, 8, 15, 16, 31, 32, 63, 64, 127, 128, 255, 256, 511, 512, 1023, 1024, 2047, 2048, 4095, 4096, 8191, 8192, 16383, 16384, 32767, 32768, 65535, 65536, 131071, 131072, 262143, 262144, 524287, 524288, 1048575, 1048576, 2097151, 2097152
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Union of A000079 and A000225 without 0 = 2^0 - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 18 2005
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FORMULA
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G.f. : 2(1+x)/(1-2x^2)-1/(1-x^2); a(n)=3a(n-2)-2a(n-4); a(n)=(1+sqrt(2)/2)(sqrt(2))^n+(1/2-sqrt(2)/2)(-sqrt(2))^n-(1+(-1)^n)/2; a(n)=sum{k=0..n, binomial(floor(n/2), floor(k/2)) }.
a(n) = 2^floor((n+2)/2) - 1 + n mod 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 18 2005
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CROSSREFS
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Sequence in context: A006049 A084541 A113050 this_sequence A116961 A120611 A092063
Adjacent sequences: A097107 A097108 A097109 this_sequence A097111 A097112 A097113
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 25 2004, corrected Sep 05 2006
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