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A156062 Riordan array (1/(1-x^4), x/(1-x^4)). 1
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 20 2009
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)