

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
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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,nk+1).
a(n) = A000204(m), where m = nt(t+1)/2, t = floor((1+sqrt(8*n7))/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(k1), ", "))) \\ 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



