A156062 Riordan array (1/(1-x^4), x/(1-x^4)).

1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 1, 1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 3, 0, 0, 0, 6, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 7, 0, 0, 0, 1, 0, 0, 0, 10, 0, 0, 0, 8, 0, 0, 0, 1, 1, 0, 0, 0, 15, 0, 0, 0, 9, 0, 0, 0, 1, 0, 4, 0, 0, 0, 21, 0, 0, 0, 10, 0, 0, 0

Offset

0,17

Comments

Row sums are A003269(n+1). Diagonal sums are the aerated Fibonacci numbers; thus

F(n+1)=sum{k=0..n, C((n+k)/2,k)*(1+(-1)^(n-k))/2}. Inverse is A156064.

Links

Table of n, a(n) for n=0..103.

Formula

Triangle T(n,k)=C((n+3k)/4,k)((1+(-1)^(n-k))/2+cos(pi*(n-k)/2))/2.

Example

Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 0, 1,
1, 0, 0, 0, 1,
0, 2, 0, 0, 0, 1,
0, 0, 3, 0, 0, 0, 1,
0, 0, 0, 4, 0, 0, 0, 1,
1, 0, 0, 0, 5, 0, 0, 0, 1,
0, 3, 0, 0, 0, 6, 0, 0, 0, 1,
0, 0, 6, 0, 0, 0, 7, 0, 0, 0, 1,
0, 0, 0, 10, 0, 0, 0, 8, 0, 0, 0, 1,
1, 0, 0, 0, 15, 0, 0, 0, 9, 0, 0, 0, 1
Production matrix of this array is
0, 1,
0, 0, 1,
0, 0, 0, 1,
1, 0, 0, 0, 1,
0, 1, 0, 0, 0, 1,
0, 0, 1, 0, 0, 0, 1,
0, 0, 0, 1, 0, 0, 0, 1,
-3, 0, 0, 0, 1, 0, 0, 0, 1,
0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
0, 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
0, 0, 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1,
-91, 0, 0, 0, 15, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1
where 1,1,-3,15,-91,612,.... is (-1)^(n-1)*C(4n-1,n)/(4n-1) (see A006632).

Crossrefs

Sequence in context: A369927 A328037 A193426 * A156064 A158757 A294890

Adjacent sequences: A156059 A156060 A156061 * A156063 A156064 A156065

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 20 2009

Status

approved