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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], 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. A000204, A104765, A104762, A104763. Cf. A027961 (row sums). Sequence in context: A076152 A107638 A245093 * A308690 A329512 A064884 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 June 19 00:22 EDT 2024. Contains 373492 sequences. (Running on oeis4.)