A048888 a(n) = Sum_{m=1..n} T(m,n+1-m), array T as in A048887.
0, 1, 2, 4, 7, 13, 23, 42, 76, 139, 255, 471, 873, 1627, 3044, 5718, 10779, 20387, 38673, 73561, 140267, 268065, 513349, 984910, 1892874, 3643569, 7023561, 13557019, 26200181, 50691977, 98182665, 190353369, 369393465, 717457655
Offset: 0
Keywords
Examples
From _Joerg Arndt_, Dec 28 2012: (Start) There are a(6)=23 compositions p(1)+p(2)+...+p(m)=6 such that p(k)<=p(1)+1: [ 1] [ 1 1 1 1 1 1 ] [ 2] [ 1 1 1 1 2 ] [ 3] [ 1 1 1 2 1 ] [ 4] [ 1 1 2 1 1 ] [ 5] [ 1 1 2 2 ] [ 6] [ 1 2 1 1 1 ] [ 7] [ 1 2 1 2 ] [ 8] [ 1 2 2 1 ] [ 9] [ 2 1 1 1 1 ] [10] [ 2 1 1 2 ] [11] [ 2 1 2 1 ] [12] [ 2 1 3 ] [13] [ 2 2 1 1 ] [14] [ 2 2 2 ] [15] [ 2 3 1 ] [16] [ 3 1 1 1 ] [17] [ 3 1 2 ] [18] [ 3 2 1 ] [19] [ 3 3 ] [20] [ 4 1 1 ] [21] [ 4 2 ] [22] [ 5 1 ] [23] [ 6 ] (End)
Links
- D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
- A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, J. Integer Seq., Vol. 9 (2006), Article 06.3.1.
Programs
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PARI
N = 66; x = 'x + O('x^N); gf = sum(n=0,N, (1-x^n)*x^n/(1-2*x+x^(n+1)) ) + 'c0; v = Vec(gf); v[1]-='c0; v /* Joerg Arndt, Apr 14 2013 */
Formula
G.f.: Sum_{k>0} x^k*(1-x^k)/(1-2*x+x^(k+1)). - Vladeta Jovovic, Feb 25 2003
a(m) = Sum_{ n=2..m+1 } Fn(m) where Fn is a Fibonacci n-step number (Fibonacci, tetranacci, etc.) indexed as in A000045, A000073, A000078. - Gerald McGarvey, Sep 25 2004
Comments