The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241819 Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that max(x(i) - x(i-1)) <= number of distinct parts of p. 5
 1, 1, 2, 3, 5, 6, 9, 11, 17, 20, 30, 37, 50, 64, 84, 106, 141, 178, 224, 290, 368, 457, 574, 722, 894, 1113, 1371, 1693, 2082, 2555, 3108, 3806, 4630, 5605, 6787, 8197, 9881, 11877, 14256, 17047, 20395, 24320, 28958, 34409, 40867, 48333, 57243, 67548, 79683 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..48. FORMULA a(n) = A241818(n) + A241820(n) for n >= 0. a(n) + A241822(n) = A000041(n) for n >= 0. EXAMPLE a(6)= 9 counts all of the 11 partitions of 6 except 51, 411. MATHEMATICA z = 30; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]]; g[p_] := Max[-Differences[p]]; Table[Count[f[n], p_ /; g[p] < d[p]], {n, 0, z}] (* A241818 *) Table[Count[f[n], p_ /; g[p] <= d[p]], {n, 0, z}] (* A241819 *) Table[Count[f[n], p_ /; g[p] == d[p]], {n, 0, z}] (* A241820 *) Table[Count[f[n], p_ /; g[p] >= d[p]], {n, 0, z}] (* A241821 *) Table[Count[f[n], p_ /; g[p] > d[p]], {n, 0, z}] (* A241822 *) CROSSREFS Cf. A241818, A241820, A241821, A241822, A000041. Sequence in context: A131995 A363066 A060714 * A227070 A032718 A366143 Adjacent sequences: A241816 A241817 A241818 * A241820 A241821 A241822 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 30 2014 STATUS approved

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

Last modified August 11 23:09 EDT 2024. Contains 375079 sequences. (Running on oeis4.)