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Search: id:A077957
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| A077957 |
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Powers of 2 alternating with zeros. |
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+0
21
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| 1, 0, 2, 0, 4, 0, 8, 0, 16, 0, 32, 0, 64, 0, 128, 0, 256, 0, 512, 0, 1024, 0, 2048, 0, 4096, 0, 8192, 0, 16384, 0, 32768, 0, 65536, 0, 131072, 0, 262144, 0, 524288, 0, 1048576, 0, 2097152, 0, 4194304, 0, 8388608, 0, 16777216, 0, 33554432, 0, 67108864, 0, 134217728, 0, 268435456
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.
Inverse binomial transform of A001333. - Paul Barry (pbarry(AT)wit.ie), Feb 25 2003
"Sloping binary representation" of powers of 2 (A000079), slope=-1 (see A037095 and A102370) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 04 2008
0,1,0,2,0,4,0,8,0,16,...is the inverse binomial transform of A000129 (Pell numbers). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]
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FORMULA
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G.f.: 1/(1-2x^2). E.g.f.: cosh(x sqrt(2)).
a(n) = (1 - n mod 2) * 2^floor(n/2).
a(n)=sqrt(2)^n*(1+(-1)^n)/2 - Paul Barry (pbarry(AT)wit.ie), May 13 2003
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PROGRAM
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(PARI) a(n)=if(n<0|n%2, 0, 2^(n/2))
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CROSSREFS
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Cf. A000079, A077966.
Sequence in context: A144775 A046666 A131575 this_sequence A077966 A021102 A021053
Adjacent sequences: A077954 A077955 A077956 this_sequence A077958 A077959 A077960
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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