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 A182747 Bisection (odd part) of number of partitions that do not contain 1 as a part A002865. 13
 0, 1, 2, 4, 8, 14, 24, 41, 66, 105, 165, 253, 383, 574, 847, 1238, 1794, 2573, 3660, 5170, 7245, 10087, 13959, 19196, 26252, 35717, 48342, 65121, 87331, 116600, 155038, 205343, 270928, 356169, 466610, 609237, 792906, 1028764, 1330772, 1716486, 2207851 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n+1) = number of partitions p of 2n 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 FORMULA a(n) = p(2*n+1)-p(2*n), where p is the partition function, A000041. - George Beck, Aug 14 2011 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+1, 2*n+1): seq(a(n), n=0..40);  # Alois P. Heinz, Dec 01 2010 MATHEMATICA f[n_] := Table[PartitionsP[2 k + 1] - PartitionsP[2 k], {k, 0, n}] (* George Beck, Aug 14 2011 *) (* also *) Table[Count[IntegerPartitions[2 n], 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+1, 2*n+1]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *) CROSSREFS Cf. A000041, A002865, A058695, A135010, A138121, A182740, A182742, A182743, A182746. Sequence in context: A164162 A164165 A164168 * A164406 A178982 A164397 Adjacent sequences:  A182744 A182745 A182746 * A182748 A182749 A182750 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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