A199512 Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers).

1, 1, 2, 2, 3, 5, 3, 5, 8, 13, 5, 8, 13, 21, 34, 8, 13, 21, 34, 55, 89, 13, 21, 34, 55, 89, 144, 233, 21, 34, 55, 89, 144, 233, 377, 610, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181

Offset: 0

Author

Philippe Deléham, Nov 07 2011

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins :
1
1, 2
2, 3, 5
3, 5, 8, 13
5, 8, 13, 21, 34
8, 13, 21, 34, 55, 89
		

Links

• Michel Marcus, Rows n=0..50 of triangle, flattened
• László Németh, On the Binomial Interpolated Triangles, Journal of Integer Sequences, Vol. 20 (2017), Article 17.7.8. See p. 15.

Crossrefs

Cf. A000045, A199334.

Rows sums : A096140, Diagonal sums : A128620.

Programs

PARI

T(n, k) = fibonacci(n+k+1);
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Aug 01 2017

Formula

T(n,k) = T(n,k-1) + T(n-1,k-1) = T(n-1,k-1) + T(n-1,k).

T(n,0) = Fibonacci(n+1) = A000045(n+1).

Extensions

More terms from Michel Marcus, Aug 01 2017