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

%I A104765 #30 Jun 21 2025 20:01:22
%S A104765 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 A104765 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 A104765 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 A104765 Triangle T(n,k) read by rows: row n contains the first n Lucas numbers A000204.
%C A104765 Reading rows from the right to the left yields A104764.
%C A104765 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 A104765 G. C. Greubel, <a href="/A104765/b104765.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H A104765 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F A104765 T(n,k) = A000204(k), 1<=k<=n.
%F A104765 T(n,k) = A104764(n,n-k+1).
%F A104765 a(n) = A000204(m), where m = n-t(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). - _Boris Putievskiy_, Dec 14 2012
%F A104765 G.f.: (x*y*(2*x*y+1))/((x-1)*(x^2*y^2+x*y-1)). - _Vladimir Kruchinin_, Jun 21 2025
%e A104765 First few rows of the triangle are:
%e A104765   1;
%e A104765   1, 3;
%e A104765   1, 3, 4;
%e A104765   1, 3, 4, 7;
%e A104765   1, 3, 4, 7, 11;
%e A104765   1, 3, 4, 7, 11, 18;
%e A104765   ...
%t A104765 Table[LucasL[k], {n, 1, 10}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Dec 21 2017 *)
%t A104765 Module[{nn=20,luc},luc=LucasL[Range[nn]];Table[Take[luc,n],{n,nn}]]//Flatten (* _Harvey P. Dale_, Jul 10 2024 *)
%o A104765 (PARI) for(n=1,10, for(k=1,n, print1(fibonacci(k+1) + fibonacci(k-1), ", "))) \\ _G. C. Greubel_, Dec 21 2017
%Y A104765 Cf. A000204, A104765, A104762, A104763.
%Y A104765 Cf. A027961 (row sums).
%K A104765 nonn,tabl,easy
%O A104765 1,3
%A A104765 _Gary W. Adamson_, Mar 24 2005
%E A104765 Edited and extended by _R. J. Mathar_, Jul 23 2008