0,4

a(n+1) is the number of noncongruent n-dimensional integer-sided simplices with diameter n. - Sascha Kurz (sascha.kurz(AT)uni-byreuth.de), Jul 26 2004

Also, the number of partitions of n into parts each less than n.

Also, the number of distinct types of equation which can be derived from the equation [n,0,0] not including itself. (Ince)

Also, the number of rooted trees on n nodes with height exactly 2.

Also, the number of partitions (of any positive integer) whose sum + length is <= n. Example: a(5) = 6 counts 4, 3, 21, 2, 11, 1. Proof: Given a partition of n other than the all 1s partition, subtract 1 from each part and then drop the zeros. This is a bijection to the partitions with sum + length <= n. - David Callan (callan(AT)stat.wisc.edu), Nov 29 2007

E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944, p. 498; MR0010757.

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

N. J. A. Sloane, Table of n, a(n) for n=0..199

with (combstruct):ZL:=proc(m) local i; [T0, {seq(T.i=Prod(Z, Set(T.(i+1))), i=0..m-1), T.m=Z}, unlabeled] end:A:=n -> count(ZL(2), size=n)-count(ZL(1), size=n): seq(A(n), n=1..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 05 2007

ZL :=[S, {S = Set(Cycle(Z), 1 < card)}, unlabelled]: seq(combstruct[count](ZL, size=n), n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008

(PARI) a(n)=if(n<0, 0, polcoeff(1/eta(x+x*O(x^n)), n)-1)

(PARI) a(n)=if(n<0, 0, numbpart(n)-1)

A000041 - 1. A diagonal of A058716.

Adjacent sequences: A000062 A000063 A000064 this_sequence A000066 A000067 A000068

Sequence in context: A103259 A082380 A136460 this_sequence A023499 A103445 A001747

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).