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Search: id:A153285
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| A153285 |
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a(n)=n^2+sum((-1)^j*a(j)); for j=1 to n-1; with a(1)=1 |
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+0
3
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| 1, 3, 11, 7, 23, 11, 35, 15, 47, 19, 59, 23, 71, 27, 83, 31, 95, 35, 107, 39, 119, 43, 131, 47, 143, 51, 155, 55, 167, 59, 179, 63, 191, 67, 203, 71, 215, 75, 227, 79, 239, 83, 251, 87, 263, 91, 275, 95, 287, 99, 299, 103, 311, 107, 323, 111, 335, 115, 347, 119, 359
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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1 followed by interleaving of A004767 and A017653. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
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FORMULA
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a(n)=2n-1 if n is 1 or an even number
a(n)=6n-7 if n is an odd number other than 1
G.f.: x*(1+3*x+9*x^2+x^3+2*x^4)/((1+x)^2*(1-x)^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
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EXAMPLE
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a(1)=1, a(2)=2^2-a(1)=4-1=3, a(3)=3^2+a(2)-a(1)=9+3-1=11, a(4)=4^2-11+3-1=7,
a(5)=25+7-11+3-1=23, a(6)=36-23+7-11+3-1=11, etc.
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PROGRAM
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(MAGMA) S:=[ 1 ]; for n in [2..61] do Append(~S, n^2 + &+[ (-1)^j*S[j]: j in [1..n-1] ]); end for; S; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
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CROSSREFS
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The second of a family of sequences that includes A153284 and A153286
Cf. A004767 (4n+3), A017653 (12n+11). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
Sequence in context: A120299 A094900 A164808 this_sequence A083557 A119324 A006495
Adjacent sequences: A153282 A153283 A153284 this_sequence A153286 A153287 A153288
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KEYWORD
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easy,nonn
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AUTHOR
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Walter Carlini (wgcarlini(AT)charter.net), Dec 23 2008
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EXTENSIONS
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Extended beyond a(30) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009
G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 15 2009
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