%I #24 Jul 10 2024 12:46:01

%S 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,

%T 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,

%U 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

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

%C Reading rows from the right to the left yields A104764.

%C 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

%H G. C. Greubel, <a href="/A104765/b104765.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.

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

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

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

%e First few rows of the triangle are:

%e 1;

%e 1, 3;

%e 1, 3, 4;

%e 1, 3, 4, 7;

%e 1, 3, 4, 7, 11;

%e 1, 3, 4, 7, 11, 18;

%e ...

%t Table[LucasL[k], {n, 1, 10}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Dec 21 2017 *)

%t Module[{nn=20,luc},luc=LucasL[Range[nn]];Table[Take[luc,n],{n,nn}]]//Flatten (* _Harvey P. Dale_, Jul 10 2024 *)

%o (PARI) for(n=1,10, for(k=1,n, print1(fibonacci(k+1) + fibonacci(k-1), ", "))) \\ _G. C. Greubel_, Dec 21 2017

%Y Cf. A000204, A104765, A104762, A104763.

%Y Cf. A027961 (row sums).

%K nonn,tabl,easy

%O 1,3

%A _Gary W. Adamson_, Mar 24 2005

%E Edited and extended by _R. J. Mathar_, Jul 23 2008