A132015
Number of partitions of n into distinct parts such that u^2 < v for all pairs (u,v) of parts with u
1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 22, 23, 24, 24, 24, 24, 24
Offset: 1
Keywords
Examples
a(10) = #{10, 9+1, 8+2, 7+2+1} = 4;
a(11) = #{11, 10+1, 9+2, 8+2+1} = 4;
a(12) = #{12, 11+1, 10+2, 9+2+1} = 4;
a(13) = #{13, 12+1, 11+2, 10+3, 10+2+1} = 5;
a(14) = #{14, 13+1, 12+2, 11+3, 11+2+1, 10+3+1} = 6;
a(15) = #{15, 14+1, 13+2, 12+3, 12+2+1, 11+3+1} = 6.
Links
- R. Zumkeller, Table of n, a(n) for n = 1..10000
Formula
a(n) = f(n,1) with f(m,p) = if p=m then 1 else (if p
A132042 Number of times record values occur in A132015.
2, 4, 1, 5, 1, 7, 1, 9, 1, 1, 1, 9, 1, 1, 1, 11, 1, 1, 1, 13, 1, 1, 1, 15, 1, 1, 1, 17, 1, 1, 1, 1, 18, 1, 1, 1, 1, 20, 1, 1, 1, 1, 22, 1, 1, 1, 1, 24, 1, 1, 1, 1, 26, 1, 1, 1, 1, 28, 1, 1, 1, 1, 30, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 33, 1, 1, 1, 1, 1, 35, 1, 1, 1, 1, 1, 37, 1, 1, 1, 1, 1, 39, 1, 1, 1, 1, 1
Offset: 1
Keywords
Comments
Crossrefs
Cf. A132088.
A132087 Where record values occur in A132085.
1, 5, 11, 19, 29, 30, 41, 42, 55, 56, 71, 72, 89, 90, 109, 110, 111, 131, 132, 133, 155, 156, 157, 181, 182, 183, 209, 210, 211, 239, 240, 241, 271, 272, 273, 305, 306, 307, 308, 341, 342, 343, 344, 379, 380, 381, 382, 419, 420, 421, 422, 461, 462, 463, 464
Offset: 1
Keywords
Comments
Crossrefs
Cf. A132017.
A132016 Record values in A132015.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 75, 77, 78, 79, 80, 81
Offset: 1
Keywords
Comments
Crossrefs
Cf. A132086.
Comments