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A104765 Triangle T(n,k) read by rows: row n contains the first n Lucas numbers A000204. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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]

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 * A064884 A093560 A173934

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

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)