A039845 Number of partitions satisfying cn(0,5) <= cn(1,5) + cn(2,5) + cn(3,5) and cn(0,5) <= cn(4,5) + cn(2,5) + cn(3,5).

1, 1, 2, 3, 5, 6, 10, 14, 21, 28, 39, 52, 72, 94, 126, 166, 217, 278, 361, 460, 593, 746, 944, 1182, 1486, 1854, 2303, 2848, 3520, 4322, 5319, 6489, 7928, 9634, 11695, 14160, 17100, 20601, 24782, 29710, 35612, 42515, 50755, 60407, 71798, 85198, 100899, 119333, 140932, 166082, 195604, 229826, 269882, 316318, 370307

Offset

0,3

Comments

For a given partition cn(i,n) means the number of its parts equal to i modulo n.

Short: 0 <= 1 + 2 + 3 and 0 <= 4 + 2 + 3 (BBpA).

Links

Table of n, a(n) for n=0..54.

Mathematica

okQ[p_] := Module[{c},
   c[k_] := c[k] = Count[Mod[p, 5], k];
   c[0] <= c[1] + c[2] + c[3] &&
   c[0] <= c[4] + c[2] + c[3]];
a[n_] := a[n] = Count[okQ /@ IntegerPartitions[n], True];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 54}] (* Jean-François Alcover, Oct 11 2024 *)

Crossrefs

Sequence in context: A325534 A280013 A039840 * A371132 A347868 A039848

Adjacent sequences: A039842 A039843 A039844 * A039846 A039847 A039848

Keyword

nonn

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Jean-François Alcover, Oct 11 2024

Status

approved