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Search: id:A130404
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| 1, 2, 3, 6, 7, 12, 13, 20, 21, 30, 31, 42, 43, 56, 57, 72, 73, 90, 91, 110, 111, 132, 133, 156, 157, 182, 183, 210, 211, 240, 241, 272, 273, 306, 307, 342, 343, 380, 381, 420, 421, 462, 463, 506, 507, 552, 553, 600, 601, 650, 651, 702, 703, 756, 757, 812, 813
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = A093178(n) - A093178(n-1).
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FORMULA
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a(1) = 1; for n > 1, a(n) = a(n-1)+1 if n is odd, a(n) = a(n-1)+(n-1) if n is even.
a(n) = A002061((n+1)/2) = (n^2+3)/4 if n is odd, a(n) = A002378(n/2) = (n^2+2*n)/4) if n is even.
G.f.: (1+x-x^2+x^3)/((1-x)^3*(1+x)^2).
a(1) = 1; a(n) = a(n-1)+n^(n mod 2) = 1/4*(n^2+2n+4+(n mod 2)*(2n-1)). - Rolf Pleisch (r_pleisch(AT)gmx.ch), Feb 04 2008
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PROGRAM
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(PARI) {s=0; for(n=1, 57, s=s+if(n%2>0, 1, n-1); print1(s, ", "))}
(PARI) {for(n=1, 57, print1(if(n%2>0, (n^2+3)/4, (n^2+2*n)/4), ", "))}
(MAGMA) &cat[ [ n^2-n+1, n*(n+1) ]: n in [1..29] ];
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CROSSREFS
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Cf. A093178, A002061, A002378.
Sequence in context: A115889 A101319 A030013 this_sequence A064689 A144120 A073712
Adjacent sequences: A130401 A130402 A130403 this_sequence A130405 A130406 A130407
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 25 2007
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