A132017 Where record values occur in A132015.
1, 3, 7, 8, 13, 14, 21, 22, 31, 32, 33, 34, 43, 44, 45, 46, 57, 58, 59, 60, 73, 74, 75, 76, 91, 92, 93, 94, 111, 112, 113, 114, 115, 133, 134, 135, 136, 137, 157, 158, 159, 160, 161, 183, 184, 185, 186, 187, 211, 212, 213, 214, 215, 241, 242, 243, 244, 245, 273, 274
Offset: 1
Keywords
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.
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.
A132085
Number of partitions of n into distinct parts such that (u+1)^2 <= v for all pairs (u,v) of parts with u
1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
Offset: 1
Keywords
Examples
a(10)=#{10,9+1}=2;
a(20)=#{20,19+1,18+2,17+3}=4;
a(30)=#{30,29+1,28+2,27+3,26+4,25+4+1}=6;
a(40)=#{40,39+1,38+2,37+3,36+4,35+4+1}=6;
a(50)=#{50,49+1,48+2,47+3,46+4,45+5,45+4+1,44+5+1}=8;
a(60)=#{60,59+1,58+2,57+3,56+4,55+5,55+4+1,54+6,54+5+1,53+6+1}=10.
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
Comments
Crossrefs