References to the Online Encyclopedia of Integer Sequences.

 Length ofoptimal rulerswith n-1 segments 0,1,3,6,9,13,17,23,29,36,43,... A004137 Optimal rulers with n segments 1,1,2,2,4,6,12,4,6,2,2,4,12,... A103299 Perfect rulerswith n segments 1,1,3,9,24,88,254,1064,1644,... A103301 Perfect rulerswith length n 1,1,1,2,3,4,2,12,8,4,38,30,... A103300 Complete rulerswith length n 1,1,1,3,4,9,17,33,63,128,248,... A103295 Complete rulerswith n segments 1,1,3,10,38,175,885,5101,32080,... A103296 Complete rulerswith length n and k segments 1,0,1,0,0,1,0,0,2,1,0,0,0,3,1,... A103294 Possible lengths ofperfect rulerswith n segments 1,1,2,3,3,4,4,6,6,7,7,7,8,10,... A103297 Segments of aperfect rulerwith length n 0,1,2,2,3,3,3,4,4,4,5,5,5,5,... A103298

Relations

T described by A103294.
A103296(n) = Sum (T(i,n), i from n to A004137(n+1)), n>=0.
A103295(n) = Sum (T(n,i), i from A103298(n) to n), n>=0.
A103300(n) = T(n, A103298(n))

A103301(n) = Sum (A103300(i), i from A004137(n)+1 to A004137(n+1)), n>=1.
A103299(n) = A103300(A004137(n+1))
A103297(n) = A004137(n+1) - A004137(n), n>= 1.

A103298(1+A004137(n)) = n

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