0,4

Diagonal sums of the "postage stamp" array: for rows n >= -1, column m >= 0 is given by F(n,m)=F(n-1,m)+F(n-2,m)+...+F(n-m,m) with F(0,m)=1 (m >= 0), F(n,m)=0 (n<0) and F(n,0)=0 (n>0). (Rows indicate the required sum, columns indicate the integers available {0,...,m}, entries F(n,m) indicate number of ordered ways sum can be achieved (eg n=3, m=2: 3=1+1+1=1+2=2+1 so F(3,2)=3 ways)). - Richard L. Ollerton (r.ollerton(AT)uws.edu.au)

Conjecture: for n>0 a(n+1) is the number of "numbral" divisors of (4^n-1)/3 = A002450(n) (see A048888 for the definition of numbral arithmetic). This has been verified computationally up to n=15. - John W. Layman (layman(AT)math.vt.edu), Dec 18 2001

R. Kemp, Balanced ordered trees, Random Structures and Alg., 5 (1994), pp. 99-121.

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

T. D. Noe, Table of n, a(n) for n=0..400

A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.1.

Index entries for sequences related to trees

Define generalized Fibonacci numbers by Sum_{h>=0} F(p, h)z^n = z^(p-1)(1-z)/(1-2z+z^p+1). Then a(n) = 1+Sum{2<=h<=n} F(h-1, n-2).

G.f.: Sum_{k>0} x^k*(1-2*x+x^2+(1-x)*x^(k+1))/(1-2*x+x^(k+1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 25 2003

F(-1,0)=0 so a(0)=0. F(0,0)=1, F(-1,1)=0 so a(1)=1. F(1,0)=0, F(0,1)=1, F(-1,2)=0 so a(2)=1. F(2,0)=0, F(1,1)=1, F(0,2)=1, F(-1,3)=0 so a(3)=2.

f[ n_, m_ ] := f[ n, m ]=Which[ n>0, Sum[ f[ n-i, m ], {i, 1, m} ], n<0, 0, n==0, 1 ] Table[ Sum[ f[ i, n-i ], {i, 0, n} ], {n, -1, 40} ]

Essentially the same as A079500. Cf. A048888.

Sequence in context: A108351 A038495 A079500 this_sequence A108296 A072100 A104882

Adjacent sequences: A007056 A007057 A007058 this_sequence A007060 A007061 A007062

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, R. Kemp

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 08 2000