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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
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. A027961 (row sums).
Sequence in context: A076152 A107638 A245093 * A308690 A329512 A064884
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 June 19 00:22 EDT 2024. Contains 373492 sequences. (Running on oeis4.)