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A228815 Symmetric triangle, read by rows, related to Fibonacci numbers. 1
0, 1, 1, 1, 2, 1, 2, 5, 5, 2, 3, 10, 14, 10, 3, 5, 20, 36, 36, 20, 5, 8, 38, 83, 106, 83, 38, 8, 13, 71, 182, 281, 281, 182, 71, 13, 21, 130, 382, 690, 834, 690, 382, 130, 21, 34, 235, 778, 1606, 2268, 2268, 1606, 778, 235, 34, 55, 420, 1546, 3586, 5780, 6750 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Triangles satisfying the same recurrence: A091533, A091562, A185081, A205575, A209137, A209138.

LINKS

Table of n, a(n) for n=0..60.

FORMULA

G.f.: x*(1+y)/(1-x-x*y-x^2-x^2*y-x^2*y^2).

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + T(n-2,k-2), T(0,0) = 0, T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.

Sum_{k = 0..n} T(n,k)*x^k = A000045(n), 2*A015518(n), 3*A015524(n), 4*A200069(n) for x = 0, 1, 2, 3 respectively.

Sum_{k = 0..floor(n/2)} T(n-k,k) = A008998(n+1).

EXAMPLE

Triangle begins :

0

1, 1

1, 2, 1

2, 5, 5, 2

3, 10, 14, 10, 3

5, 20, 36, 36, 20, 5

8, 38, 83, 106, 83, 38, 8

13, 71, 182, 281, 281, 182, 71, 13

21, 130, 382, 690, 834, 690, 382, 130, 21

34, 235, 778, 1606, 2268, 2268, 1606, 778, 235, 34

55, 420, 1546, 3586, 5780, 6750, 5780, 3586, 1546, 420, 55

CROSSREFS

Cf. A000045 (1st column), A001629 (2nd column), A008998, A152011, A261055 (3rd column).

Sequence in context: A328601 A137327 A143913 * A241555 A277741 A241138

Adjacent sequences:  A228812 A228813 A228814 * A228816 A228817 A228818

KEYWORD

nonn,easy,tabl

AUTHOR

Philippe Deléham, Oct 30 2013

STATUS

approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)