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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) is the 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 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, and Gideon Vos, Large-N correlation functions in N = 2 superconformal QCD, arXiv preprint arXiv:1610.07612 [hep-th], 2016. K. Blum, Bounds on the Number of Graphical Partitions, arXiv:2103.03196 [math.CO], 2021. See Table on p. 7. FORMULA a(n) = p(2*n) - p(2*n-1), where p is the partition function, A000041. - George Beck, Jun 05 2017 [Shifted by Georg Fischer, Jun 20 2022] 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-François Alcover, Sep 21 2015, after Alois P. Heinz *) a[n_] := PartitionsP[2*n] - PartitionsP[2*n - 1]; Table[a[n], {n, 0, 40}] (* George Beck, Jun 05 2017 *) PROG (PARI) a(n)=numbpart(2*n)-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: A178937 A168368 A305106 * A100482 A301762 A003293 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 December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)