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A182735 Number of parts in all partitions of 2n+1 that do not contain 1 as a part. 3
0, 1, 3, 8, 20, 41, 80, 153, 271, 469, 795, 1305, 2102, 3336, 5190, 7968, 12090, 18104, 26821, 39371, 57220, 82472, 117958, 167405, 235945, 330425, 459803, 636142, 875307, 1197983, 1631470, 2211377, 2983695, 4008386, 5362831, 7146335, 9486834, 12548085, 16538651 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

MAPLE

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

      if n<0 then [0, 0]

    elif n=0 then [1, 0]

    elif i<2 then [0, 0]

    else p, q:= b(n, i-1), b(n-i, i);

        [p[1]+q[1], p[2]+q[2]+q[1]]

      fi

    end:

a:= n-> b(2*n+1, 2*n+1)[2]:

seq(a(n), n=0..35);  # Alois P. Heinz, Dec 03 2010

MATHEMATICA

b[n_, i_] := b[n, i] = Module[{p, q}, Which[n<0, {0, 0}, n == 0, {1, 0}, i < 2, {0, 0}, True, {p, q} = {b[n, i-1], b[n-i, i]}; {p[[1]] + q[[1]], p[[2]] + q[[2]] + q[[1]]}]]; a[n_] := b[2*n+1, 2*n+1][[2]]; Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Oct 29 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A135010, A138121, A182734, A182743, A182747. Bisection (odd part) of A138135.

Sequence in context: A321067 A224421 A143785 * A135565 A139488 A028307

Adjacent sequences:  A182732 A182733 A182734 * A182736 A182737 A182738

KEYWORD

nonn

AUTHOR

Omar E. Pol, Dec 03 2010

EXTENSIONS

More terms from Alois P. Heinz, Dec 03 2010

STATUS

approved

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Last modified May 12 06:20 EDT 2021. Contains 343814 sequences. (Running on oeis4.)