A178304 Triangle T(n,m) = 1 + f(n+1)*(f(m+1) + f(n-m+1) - 1 - f(n+1)), read by rows, where f(.)=A002487(.).

1, 1, 1, 1, -1, 1, 1, 2, 2, 1, 1, -5, 1, -5, 1, 1, 3, 1, 1, 3, 1, 1, -2, 4, -5, 4, -2, 1, 1, 3, 3, 3, 3, 3, 3, 1, 1, -11, 1, -7, 5, -7, 1, -11, 1, 1, 4, -2, 1, 4, 4, 1, -2, 4, 1, 1, -9, 1, -19, 1, -9, 1, -19, 1, -9, 1

Offset

0,8

Comments

Row sums are 1, 2, 1, 6, -7, 10, 1, 20, -27, 16, -59, ...

Links

Table of n, a(n) for n=0..65.

Example

Rows n >= 0, 0 <= k <= n begin
  1;
  1,   1;
  1,  -1,   1;
  1,   2,   2,   1;
  1,  -5,   1,  -5,   1;
  1,   3,   1,   1,   3,   1;
  1,  -2,   4,  -5,   4,  -2,   1;
  1,   3,   3,   3,   3,   3,   3,   1;
  1, -11,   1,  -7,   5,  -7,   1, -11,   1;
  1,   4,  -2,   1,   4,   4,   1,  -2,   4,   1;
  1,  -9,   1, -19,   1,  -9,   1, -19,   1,  -9,   1;

Maple

A002487 := proc(n) option remember; if n <=1 then n; else if type(n, 'even') then procname(n/2) ; else procname((n-1)/2)+procname(1+(n-1)/2) ; end if; end if; end proc:
A178304 := proc(n, m) 1 + A002487(n+1)*( A002487(m+1)+A002487(n-m+1)-1-A002487(n+1) ) ; end proc:
seq(seq(A178304(n, k), k=0..n), n=0..15) ; # N. J. A. Sloane, Jul 20 2010

Mathematica

a[0] = 0; a[1] = 1;
a[n_] := a[n] = If[Mod[n, 2] == 0, a[Floor[n/2]], a[ Floor[(n - 1)/2]] + a[Floor[(n + 1)/2]]];
tg[n_, m_] := 1 + a[n + 1]*a[m + 1] + a[n + 1]*a[n - m + 1] - (a[n + 1]*a[ 0 + 1] + a[n + 1]*a[n - 0 + 1]);
Table[Table[tg[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A002487, A177443.

Sequence in context: A209543 A178655 A337278 * A123585 A145668 A318405

Adjacent sequences: A178301 A178302 A178303 * A178305 A178306 A178307

Keyword

sign,tabl,easy

Author

Roger L. Bagula and Gary W. Adamson, May 24 2010

Extensions

Definition simplified by the Assoc. Eds. of the OEIS, Jul 20 2010

Status

approved