A139040 - OEIS

%I #20 Apr 26 2017 22:58:05

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,2,3,2,1,1,1,1,2,3,3,2,

%T 1,1,1,1,2,3,4,3,2,1,1,1,1,2,3,4,4,3,2,1,1,1,1,2,3,4,6,4,3,2,1,1,1,1,

%U 2,3,4,6,6,4,3,2,1,1,1,1,2,3,4,6,9,6,4,3,2,1,1,1,1,2,3,4,6,9,9,6,4,3,2,1,1

%N Triangle read by rows: each row is an initial segment of the terms of A000930 followed by its reflection.

%H G. C. Greubel, <a href="/A139040/b139040.txt">Table of n, a(n) for the first 100 rows, flattened</a>

%e Triangle begins:

%e {1},

%e {1, 1},

%e {1, 1, 1},

%e {1, 1, 1, 1},

%e {1, 1, 2, 1, 1},

%e {1, 1, 2, 2, 1, 1},

%e {1, 1, 2, 3, 2, 1, 1},

%e {1, 1, 2, 3, 3, 2, 1, 1},

%e {1, 1, 2, 3, 4, 3, 2, 1, 1},

%e {1, 1, 2, 3, 4, 4, 3, 2, 1, 1},

%e {1, 1, 2, 3, 4, 6, 4, 3, 2, 1, 1}

%p A000930 := proc(n) coeftayl( 1/(1-x-x^3),x=0,n) ; end: A139040 := proc(n,m) A000930(min(m,n+1-m)) ; end: for n from 1 to 16 do for m from 1 to n do printf("%d,",A139040(n,m)) ; od: od: # _R. J. Mathar_, Jun 08 2008

%t a[-2]=0;a[-1]=1;a[0]=1;a[n_]:=a[n]=a[n-1]+a[n-3];(*A000930*)

%t g[n_,m_]:=If[m <= Floor[n/2],a[m],a[n-m]];w=Table[Table[g[n,m],{m,0,n}],{n,0,10}]; Flatten[w]

%Y Cf. A139147, A000930. Row sums are in A238383.

%K nonn,easy,tabl

%O 1,13

%A _Roger L. Bagula_ and _Gary W. Adamson_, May 31 2008

%E Edited and corrected by _N. J. A. Sloane_, Jun 30 2008

%E Corrected by _Philippe Deléham_, Feb 25 2014