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

0,3

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.

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).

Example

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

Prog

(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

Crossrefs

Cf. A000045, A199334.

Rows sums : A096140, Diagonal sums : A128620.

Sequence in context: A067330 A202874 A355197 * A303969 A304931 A304669

Adjacent sequences: A199509 A199510 A199511 * A199513 A199514 A199515

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Nov 07 2011

Extensions

More terms from Michel Marcus, Aug 01 2017

Status

approved