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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

Sequence in context: A103259 A082380 A136460 this_sequence A023499 A103445 A001747

Adjacent sequences: A000062 A000063 A000064 this_sequence A000066 A000067 A000068

nonn,easy

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