%I
%S 3,3,7,10,17,25,40,57,85,121,172,240,335,459,630,856,1160,1564,2105,
%T 2821,3777,5044,6728,8961,11926,15854,21066,27972,37127,49258,65336,
%U 86636,114862,152256,201800,267436,354394,469591,622205,824379,1092211
%N Size of the BDD for the hidden weighted bit function, with the variables in their natural ordering.
%D Beate Bollig, Martin Löbbing, Martin Sauerhoff and Ingo Werner, On the complexity of the hidden weighted bit function for various BDD models, Theoretical Informatics and Applications, 33 (1999), 103115, Theorem 4.4.
%D Randal E. Bryant, "On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication," IEEE Transactions on Computers C40 (1991), 205213.
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%H T. D. Noe, <a href="/A136445/b136445.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,3,2,2,2,0,1).
%F a(n) = (56*P(n+2)+77*P(n+1)+47*P(n))/23  floor(n^2/4)  floor((7*n+1)/3) + (n mod 2)  10, where P = A001608.  _Don Knuth_, Dec 09 2008
%F G.f.: x*(x^8+x^72*x^63*x^52*x^4+3*x^3+2*x^23) / ((x1)^3*(x+1)*(x^2+x+1)*(x^3+x^21)).  _Colin Barker_, Jan 29 2013
%e By the first formula: a(9) = (56*A001608(11)+77*A001608(10) + 47*A001608(9))/23  floor(9^2/4)  floor((7*9+1)/3) + (9 mod 2)  10 = 135  20  21 + 1  10 = 85.  _Bruno Berselli_, Jan 31 2013
%t p[n_] := n*Sum[Binomial[k, n2*k]/k, {k, 1, n/2}]; a[n_] := (56*p[n+2] + 77*p[n+1] + 47*p[n])/23  Floor[n^2/4]  Floor[(7*n+1)/3] + Mod[n, 2]  10; Table[a[n], {n, 1, 41}] (* _JeanFrançois Alcover_, Jan 31 2013 *)
%t LinearRecurrence[{1, 2, 0, 3, 2, 2, 2, 0, 1}, {3, 3, 7, 10, 17, 25, 40, 57, 85}, 50] (* _Vincenzo Librandi_, Aug 09 2015 *)
%o (MAGMA) I:=[3,3,7,10,17,25,40,57,85]; [n le 9 select I[n] else Self(n1)+2*Self(n2)3*Self(n4)2*Self(n5)+2*Self(n6)+2*Self(n7)Self(n9): n in [1..45]]; // _Vincenzo Librandi_, Aug 09 2015
%Y Cf. A137202.
%K nonn,easy
%O 1,1
%A _Don Knuth_, Apr 04 2008
%E Bryant reference added by _Don Knuth_, Apr 23 2008
%E Extension from _T. D. Noe_, Dec 10 2008
