A214582 Riordan array (1/(1-x-x^2), x*(1+2*x)).

1, 1, 1, 2, 3, 1, 3, 4, 5, 1, 5, 7, 10, 7, 1, 8, 11, 15, 20, 9, 1, 13, 18, 25, 35, 34, 11, 1, 21, 29, 40, 55, 75, 52, 13, 1, 34, 47, 65, 90, 125, 143, 74, 15, 1, 55, 76, 105, 145, 200, 275, 247, 100, 17, 1

Offset

0,4

Comments

First column is A000045 (Fibonacci numbers) starting with 1.

Second column is A000032 (Lucas numbers) starting with 1.

Links

Table of n, a(n) for n=0..54.

Formula

T(n,0) = T(n-1,0) + T(n-2,0), T(n,k) = T(n-1,k-1) + 2*T(n-2,k-1) for k>0.

Sum_{k, 0<=k<=n} T(n,k) = A094687(n+2).

T(2n,n) = A081567(n).

Example

Triangle begins
1
1, 1
2, 3, 1
3, 4, 5, 1
5, 7, 10, 7, 1
8, 11, 15, 20, 9, 1
13, 18, 25, 35, 34, 11, 1
21, 29, 40, 55, 75, 52, 13, 1
34, 47, 65, 90, 125, 143, 74, 15, 1
55, 76, 105, 145, 200, 275, 247, 100, 17, 1
...
Production array begins
1, 1
1, 2, 1
-2, -4, 2, 1
8, 16, -4, 2, 1
-40, -80, 16, -4, 2, 1
224, 448, -80, 16, -4, 2, 1
-1344, -2688, 448, -80, 16, -4, 2, 1
8448, 16896, -2688, 448, -80, 16, -4, 2, 1
... which is based on A052701.

Crossrefs

Cf. A000032, A000045, A002522, A005408, A104726, A123265

Sequence in context: A185312 A185311 A338764 * A362502 A050375 A300724

Adjacent sequences: A214579 A214580 A214581 * A214583 A214584 A214585

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 06 2013

Status

approved