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 A104762 Triangle read by rows: row n contains first n nonzero Fibonacci numbers in decreasing order. 10
 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 3, 2, 1, 1, 8, 5, 3, 2, 1, 1, 13, 8, 5, 3, 2, 1, 1, 21, 13, 8, 5, 3, 2, 1, 1, 34, 21, 13, 8, 5, 3, 2, 1, 1, 55, 34, 21, 13, 8, 5, 3, 2, 1, 1, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1, 1, 144, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1, 1, 233, 144, 89, 55, 34, 21, 13, 8, 5, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Sum of n-th row = F(n+2) - 1; sequence A000071 starting (1, 2, 4, 7, 12, 20,...). Riordan array (1/(1-x-x^2),x) . [Philippe Deléham, Apr 23 2009] Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order. Sequence A104762 is the reverse reluctant sequence of Fibonacci numbers (A000045), except 0. - Boris Putievskiy, Dec 13 2012 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO] FORMULA In every column, (1, 1, 2, 3, 5,...); the nonzero Fibonacci numbers, A000045. a(n,k) = A000045(n-k+1). - R. J. Mathar, Jun 23 2006 a(n)=A000045(m), where m=(t*t+3*t+4)/2-n, t=floor[(-1+sqrt(8*n-7))/2]. - Boris Putievskiy, Dec 13 2012 Let P denote Pascal's triangle. Then P*A104762*P^(-1 ) = A121461. - Peter Bala, Apr 11 2013 a(n,k) = |round[(r^n)*(s^k)/sqrt(5)|, where r = golden ratio = (1+ sqrt(5))/2, s = (1 - sqrt(5))/2, 1 < = k <= n-1, n > = 2. - Clark Kimberling, May 01 2016 G.f. of triangle: G(x,y) = x*y/((1-x-x^2)*(1-x*y)). - Robert Israel, May 01 2016 EXAMPLE First few rows of the triangle are: 1; 1, 1; 2, 1, 1; 3, 2, 1, 1; 5, 3, 2, 1, 1; 8, 5, 3, 2, 1, 1; ... Production matrix begins: 1, 1 1, 0, 1 0, 0, 0, 1 0, 0, 0, 0, 1 0, 0, 0, 0, 0, 1 0, 0, 0, 0, 0, 0, 1 0, 0, 0, 0, 0, 0, 0, 1 ... - Philippe Deléham, Oct 07 2014 MAPLE seq(seq(combinat:-fibonacci(n-i), i=0..n-1), n=1..20); # Robert Israel, May 01 2016 MATHEMATICA r = N[(1 + Sqrt[5])/2, 100]; s = N[(1 - Sqrt[5])/2, 100]; t = Table[Abs[Round[(r^n)*(s^k)/Sqrt[5]]], {n, 2, 15}, {k, 1, n - 1}] Flatten[t] TableForm[t] (* Clark Kimberling, May 01 2016 *) Table[Reverse[Fibonacci[Range[n]]], {n, 15}]//Flatten (* Harvey P. Dale, Jan 28 2019 *) CROSSREFS Cf. A000045, A000071, A271355 (analogous Lucas triangle). Companion triangle A104763, Fibonacci sequence in each row starting from the left. A121461. Sequence in context: A194543 A287920 A027293 * A152462 A180360 A318805 Adjacent sequences:  A104759 A104760 A104761 * A104763 A104764 A104765 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Mar 23 2005, Mar 05 2007 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Philippe Deléham, Jun 11 2007 More terms from Philippe Deléham, Apr 21 2009 STATUS approved

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)