The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209815 Number of partitions of 2n in which every part is
 0, 1, 4, 10, 23, 47, 90, 164, 288, 488, 807, 1303, 2063, 3210, 4920, 7434, 11098, 16380, 23928, 34624, 49668, 70667, 99795, 139935, 194930, 269857, 371413, 508363, 692195, 937838, 1264685, 1697810, 2269557, 3021462, 4006812, 5293650, 6968730, 9142306, 11954194 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A008284(3*n-1,n-1). - Hans Loeblich Apr 18 2019 EXAMPLE The 4 partitions of 6 with parts <3: 2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1. Matching partitions of 2 into rationals as described: 2/3 + 2/3 + 2/3 2/3 + 2/3 + 1/3 + 1/3 2/3 + 1/3 + 1/3 + 1/3 + 1/3 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3. MAPLE b:= proc(n, i) option remember; `if`(n=0, 1,       `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i))))     end: a:= n-> b(2*n, n-1): seq(a(n), n=1..50);  # Alois P. Heinz, Jul 09 2012 MATHEMATICA f[n_] := Length[Select[IntegerPartitions[2 n], First[#] <= n - 1 &]];  Table[f[n], {n, 1, 34}]  (* A209815 *) b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i]]]]; a[n_] := b[2*n, n-1]; Table [a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 28 2015, after Alois P. Heinz *) PROG (Haskell) a209815 n = p [1..n-1] (2*n) where    p _          0 = 1    p []         _ = 0    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m -- Reinhard Zumkeller, Nov 14 2013 CROSSREFS Cf. A209816. Cf. A231429. Sequence in context: A305102 A008268 A084446 * A158671 A001980 A266376 Adjacent sequences:  A209812 A209813 A209814 * A209816 A209817 A209818 KEYWORD nonn AUTHOR Clark Kimberling, Mar 13 2012 EXTENSIONS More terms from Alois P. Heinz, Jul 09 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 04:43 EST 2021. Contains 349400 sequences. (Running on oeis4.)