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A171729 Triangle of differences of Fibonacci numbers, rows ascending.

%I A171729 #19 Jan 13 2025 08:22:40
%S A171729 1,1,2,1,2,3,2,3,4,5,3,5,6,7,8,5,8,10,11,12,13,8,13,16,18,19,20,21,13,
%T A171729 21,26,29,31,32,33,34,21,34,42,47,50,52,53,54,55,34,55,68,76,81,84,86,
%U A171729 87,88,89,55,89,110,123,131,136,139,141,142,143,144,89,144,178,199,212,220,225,228,230,231,232,233
%N A171729 Triangle of differences of Fibonacci numbers, rows ascending.
%C A171729 The numbers missing from this triangle form A050939.
%C A171729 Row n of this triangle has one more term than row n of A143061.
%C A171729 Reversing the rows gives A171730.
%H A171729 Michael De Vlieger, <a href="/A171729/b171729.txt">Table of n, a(n) for n = 1..11325</a> (rows n = 1..150, flattened)
%F A171729 Counting the top row as the first row, the n-th row is
%F A171729 F(n+1)-F(n), F(n+1)-F(n-1), ..., F(n+1)-F(2), F(n+1)-F(0).
%e A171729 First rows:
%e A171729   1
%e A171729   1 2
%e A171729   1 2  3
%e A171729   2 3  4  5
%e A171729   3 5  6  7  8
%e A171729   5 8 10 11 12 13
%e A171729   ...
%p A171729 F:= combinat[fibonacci]:
%p A171729 T:= (n,k)-> F(n+1)-`if`(k=n, 0, F(n-k+1)):
%p A171729 seq(seq(T(n,k), k=1..n), n=1..12);  # _Alois P. Heinz_, Feb 06 2023
%t A171729 Table[Fibonacci[n + 1] - If[k < n, Fibonacci[n - k + 1], 0], {n, 12}, {k, n}] // Flatten (* _Michael De Vlieger_, Feb 06 2023 *)
%o A171729 (PARI) row(n) = vector(n, k, fibonacci(n+1) - if (k<n, fibonacci(n-k+1), 0)); \\ _Michel Marcus_, Feb 06 2023
%Y A171729 Cf. A000045, A050939, A143061, A171730.
%K A171729 nonn,tabl
%O A171729 1,3
%A A171729 _Clark Kimberling_, Dec 16 2009