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Search: id:A088954
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| A088954 |
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G.f.: 1/((1-x)^2*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16)). |
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+0
3
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| 1, 2, 4, 6, 10, 14, 20, 26, 36, 46, 60, 74, 94, 114, 140, 166, 202, 238, 284, 330, 390, 450, 524, 598, 692, 786, 900, 1014, 1154, 1294, 1460, 1626, 1827, 2028, 2264, 2500, 2780, 3060, 3384, 3708, 4088, 4468, 4904, 5340, 5844, 6348, 6920, 7492, 8148, 8804, 9544
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
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MAPLE
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f := proc(n, k) option remember; if k > n then RETURN(0); fi; if k= 0 then if n=0 then RETURN(1) else RETURN(0); fi; fi; if k = 1 then RETURN(1); fi; if n mod 2 = 1 then RETURN(f(n-1, k)); fi; f(n-1, k)+f(n/2, k-1); end; # present sequence is f(2m, 6)
GFF := k->x^(2^(k-2))/((1-x)*mul((1-x^(2^j)), j=0..k-2)); # present g.f. is GFF(6)/x^16
a:= proc(n) local m, r; m:= iquo (n, 16, 'r'); r:= r+1; [1, 2, 4, 6, 10, 14, 20, 26, 36, 46, 60, 74, 94, 114, 140, 166][r] +(((((128/5*m +8*(15+r))*m +(228 +[0, 32, 68, 104, 144, 184, 228, 272, 320, 368, 420, 472, 528, 584, 644, 704][r]))*m +(172 +[0, 43, 98, 153, 223, 293, 378, 463, 566, 669, 790, 911, 1053, 1195, 1358, 1521][r]))*m +(247/5 +[0, 22, 55, 88, 138, 188, 255, 322, 415, 508, 627, 746, 900, 1054, 1243, 1432][r]))*m)/3 end: seq (a(n), n=0..60); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 17 2009]
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CROSSREFS
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See A000027, A002620, A008804, A088932, A000123 for similar sequences.
Sequence in context: A008804 A001307 A088932 this_sequence A000123 A103257 A103259
Adjacent sequences: A088951 A088952 A088953 this_sequence A088955 A088956 A088957
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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), Dec 02 2003
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