A104765 Triangle T(n,k) read by rows: row n contains the first n Lucas numbers A000204.

1, 1, 3, 1, 3, 4, 1, 3, 4, 7, 1, 3, 4, 7, 11, 1, 3, 4, 7, 11, 18, 1, 3, 4, 7, 11, 18, 29, 1, 3, 4, 7, 11, 18, 29, 47, 1, 3, 4, 7, 11, 18, 29, 47, 76, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 1, 3, 4, 7, 11

Offset

1,3

Comments

Reading rows from the right to the left yields A104764.

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. Sequence A104765 is the reluctant sequence of A000204. - Boris Putievskiy, Dec 14 2012

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

T(n,k) = A000204(k), 1<=k<=n.

T(n,k) = A104764(n,n-k+1).

a(n) = A000204(m), where m = n-t(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 14 2012

Example

First few rows of the triangle are:
1;
1, 3;
1, 3, 4;
1, 3, 4, 7;
1, 3, 4, 7, 11;
1, 3, 4, 7, 11, 18;
...

Mathematica

Table[LucasL[k], {n, 1, 10}, {k, 1, n}] // Flatten (* G. C. Greubel, Dec 21 2017 *)

Prog

(PARI) for(n=1, 10, for(k=1, n, print1(fibonacci(k+1) + fibonacci(k-1), ", "))) \\ G. C. Greubel, Dec 21 2017

Crossrefs

Cf. A000204, A104765, A104762, A104763.

Cf. A027961 (row sums).

Sequence in context: A076152 A107638 A245093 * A308690 A329512 A064884

Adjacent sequences: A104762 A104763 A104764 * A104766 A104767 A104768

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Mar 24 2005

Extensions

Edited and extended by R. J. Mathar, Jul 23 2008

Status

approved