A139040 Triangle read by rows: each row is an initial segment of the terms of A000930 followed by its reflection.

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, 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, 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

Offset

1,13

Links

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Example

Triangle begins:
{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, 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}

Maple

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

Mathematica

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

Crossrefs

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

Sequence in context: A306741 A274193 A238384 * A139147 A055801 A155050

Adjacent sequences: A139037 A139038 A139039 * A139041 A139042 A139043

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Gary W. Adamson, May 31 2008

Extensions

Edited and corrected by N. J. A. Sloane, Jun 30 2008

Corrected by Philippe Deléham, Feb 25 2014

Status

approved