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A088932
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G.f.: 1/((1-x)^2*(1-x^2)*(1-x^4)*(1-x^8)).
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3
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1, 2, 4, 6, 10, 14, 20, 26, 36, 46, 60, 74, 94, 114, 140, 166, 201, 236, 280, 324, 380, 436, 504, 572, 656, 740, 840, 940, 1060, 1180, 1320, 1460, 1625, 1790, 1980, 2170, 2390, 2610, 2860, 3110, 3396, 3682, 4004, 4326, 4690, 5054, 5460, 5866, 6321, 6776, 7280, 7784
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
Index to sequences with linear recurrences with constant coefficients, signature (2,0,-2,2,-2,0,2,0,-2,0,2,-2,2,0,-2,1).
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MAPLE
| 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, 5)
GFF := k->x^(2^(k-2))/((1-x)*mul((1-x^(2^j)), j=0..k-2)); # present g.f. is GFF(5)/x^8
a:= proc(n) local m, r; m := iquo (n, 8, 'r'); r:= r+1; [1, 2, 4, 6, 10, 14, 20, 26][r]+ (((8/3*m +(4*r +28)/3)*m +[0, 4, 9, 14, 20, 26, 33, 40][r] +43/3)*m +[22, 33, 50, 67, 93, 119, 154, 189][r]/3)*m end: seq (a(n), n=0..60); # Alois P. Heinz, Apr 17 2009
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MATHEMATICA
| CoefficientList[Series[1/((1-x)^2(1-x^2)(1-x^4)(1-x^8)), {x, 0, 60}], x] (* From Harvey P. Dale, Apr 22 2011 *)
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PROG
| (PARI) Vec(1/((1-x)^2*(1-x^2)*(1-x^4)*(1-x^8))+O(x^99)) \\ Charles R Greathouse IV, Sep 03 2011
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CROSSREFS
| See A000027, A002620, A008804, A088954, A000123 for similar sequences.
Sequence in context: A115065 A008804 A001307 * A088954 A000123 A103257
Adjacent sequences: A088929 A088930 A088931 * A088933 A088934 A088935
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 02 2003
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