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A182734 Number of parts in all partitions of 2n that do not contain 1 as a part. 5


%S 0,1,3,8,17,34,68,123,219,382,642,1055,1713,2713,4241,6545,9950,14953,

%T 22255,32752,47774,69104,99114,141094,199489,280096,390836,542170,

%U 747793,1025912,1400425,1902267,2572095,3462556,4641516,6196830,8241460,10919755,14416885

%N Number of parts in all partitions of 2n that do not contain 1 as a part.

%C Essentially this is a bisection (even part) of A138135.

%H Alois P. Heinz, <a href="/A182734/b182734.txt">Table of n, a(n) for n = 0..1000</a>

%p b:= proc(n,i) option remember; local p,q;

%p if n<0 then [0,0]

%p elif n=0 then [1,0]

%p elif i=1 then [0,0]

%p else p, q:= b(n,i-1), b(n-i,i);

%p [p[1]+q[1], p[2]+q[2]+q[1]]

%p fi

%p end:

%p a:= n-> b(2*n, 2*n)[2]:

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Dec 03 2010

%t Table[Length[Flatten[DeleteCases[IntegerPartitions[2n],_?(MemberQ[ #,1]&)]]], {n,0,40}] (* _Harvey P. Dale_, Aug 08 2013 *)

%t b[n_] := DivisorSigma[0, n]-1+Sum[(DivisorSigma[0, k]-1)*(PartitionsP[n-k] - PartitionsP[n-k-1]), {k, 1, n-1}]; a[0] = 0; a[n_] := b[2n]; Table[a[n], {n, 0, 35}]

%Y Cf. A135010, A138121, A138135, A182742.

%K nonn

%O 0,3

%A _Omar E. Pol_, Dec 03 2010

%E More terms from _Alois P. Heinz_, Dec 03 2010

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)