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A182746 Bisection (even part) of number of partitions that do not contain 1 as a part A002865. 14
1, 1, 2, 4, 7, 12, 21, 34, 55, 88, 137, 210, 320, 478, 708, 1039, 1507, 2167, 3094, 4378, 6153, 8591, 11914, 16424, 22519, 30701, 41646, 56224, 75547, 101066, 134647, 178651, 236131, 310962, 408046, 533623, 695578, 903811, 1170827, 1512301, 1947826, 2501928 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1) = number of partitions p of 2n-1 such that (number of parts of p) is a part of p, for n >=0. - Clark Kimberling, Mar 02 2014

REFERENCES

Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, Gideon Vos, Large-N correlation functions in N = 2 superconformal QCD, arXiv preprint arXiv:1610.07612, 2016

LINKS

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

FORMULA

a(n) = p(2*n+2)-p(2*n+1), where p is the partition function, A000041. - George Beck, Jun 05 2017

MAPLE

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

      if n<0 then 0

    elif n=0 then 1

    elif i<2 then 0

    else b(n, i-1) +b(n-i, i)

      fi

    end:

a:= n-> b(2*n, 2*n):

seq(a(n), n=0..40);  # Alois P. Heinz, Dec 01 2010

MATHEMATICA

Table[Count[IntegerPartitions[2 n -1], p_ /; MemberQ[p, Length[p]]], {n, 20}]   (* Clark Kimberling, Mar 02 2014 *)

b[n_, i_] := b[n, i] = Which[n<0, 0, n==0, 1, i<2, 0, True, b[n, i-1] + b[n-i, i]]; a[n_] := b[2*n, 2*n]; Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Sep 21 2015, after Alois P. Heinz *)

a[n_] := PartitionsP[2 n + 2] - PartitionsP[2 n + 1]; Table[a[n], {n, 0, 40}] - George Beck, Jun 05 2017

PROG

(PARI) a(n)=numbpart(2*n+2)-numbpart(2*n+1) \\ Charles R Greathouse IV, Jun 06 2017

CROSSREFS

Cf. A000041, A002865, A058696, A135010, A138121, A182740, A182742, A182743, A182747.

Sequence in context: A079816 A178937 A168368 * A100482 A003293 A192759

Adjacent sequences:  A182743 A182744 A182745 * A182747 A182748 A182749

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Dec 01 2010

EXTENSIONS

More terms from Alois P. Heinz, Dec 01 2010

STATUS

approved

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Last modified November 18 05:08 EST 2017. Contains 294853 sequences.