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A199512 Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers). 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 04:29 EST 2022. Contains 358649 sequences. (Running on oeis4.)