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a(n) = A011782(n) + A000219(n) - A000712(n).
1

%I #10 Mar 25 2014 04:19:34

%S 1,0,0,0,1,4,15,40,103,238,531,1131,2362,4811,9694,19307,38243,75400,

%T 148443,291984,574724,1132368,2234617,4416937,8745567,17343737,

%U 34446090,68500682,136374947,271755878,541950747,1081467319,2159170372,4312555339,8616279482,17219151572,34418065540,68805730450,137566021077

%N a(n) = A011782(n) + A000219(n) - A000712(n).

%C Old definition was "Counts compositions plus plane partitions less partitions into parts of two kinds".

%C A116600 is essentially A115981 + A115982 since A000712 = A001523 + A006330.

%F a(n) = A011782(n) + A000219(n) - A000712(n).

%e a(8) = 103 because A011782(8) + A000219(8) - A000712(8) = 128 + 160 - 185.

%o (PARI)

%o N=66; x='x+O('x^N);

%o gf011782 =(1-x)/(1-2*x);

%o gf000219 = 1/prod(n=1,N, (1-x^n)^n );

%o gf000712 = 1/eta(x)^2;

%o Vec( gf011782 + gf000219 - gf000712 )

%o \\ _Joerg Arndt_, Mar 25 2014

%Y Cf. A000219, A000712, A001523, A006330, A011782, A115981, A115982.

%K easy,nonn

%O 0,6

%A _Alford Arnold_, Feb 18 2006

%E Terms a(9) and beyond from _Joerg Arndt_, Mar 25 2014