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A008810
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Ceiling(n^2/3).
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5
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0, 1, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75, 86, 97, 108, 121, 134, 147, 162, 177, 192, 209, 226, 243, 262, 281, 300, 321, 342, 363, 386, 409, 432, 457, 482, 507, 534, 561, 588, 617, 646, 675, 706, 737, 768, 801, 834, 867, 902, 937, 972, 1009, 1046
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, number of red blocks in Fig 2.5.
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LINKS
| S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta and K.M. Tamizhmani, Blending two discrete integrability criteria: ...
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FORMULA
| Euler transform of length 6 sequence [ 2, 0, 2, 0, 0, -1]. - Michael Somos Aug 03 2006
a(-n)=a(n)=ceiling(n^2/3).
G.f.: x*(1+x^3)/((1-x)^2*(1-x^3)) = x*(1-x^6)/((1-x)*(1-x^3))^2.
a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=6, a(n)=2*a(n-1)-a(n-2)+a(n-3)- 2*a(n-4)+a(n-5) [From Harvey P. Dale, June 20 2011]
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MATHEMATICA
| Ceiling[Range[0, 100]^2/3] (*From Vladimir Joseph Stephan Orlovsky, Mar 15 2011*)
LinearRecurrence[{2, -1, 1, -2, 1}, {0, 1, 2, 3, 6}, 60] (* From Harvey P. Dale, June 20 2011 *)
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PROG
| (PARI) a(n)=ceil(n^2/3) /* Michael Somos Aug 03 2006 */
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CROSSREFS
| A056105(n)=a(3n-1). A056109(n)=a(3n+1). - Michael Somos Aug 03 2006.
Sequence in context: A077121 A140495 A174873 * A176893 A144677 A058616
Adjacent sequences: A008807 A008808 A008809 * A008811 A008812 A008813
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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