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A119444 Triangle as described in A100461, except with t(1,n) = Fibonacci(n+1).

%I A119444 #10 Apr 07 2023 08:57:40
%S A119444 1,1,2,1,2,3,1,2,3,5,1,2,3,4,8,3,4,6,8,10,13,7,8,9,12,15,18,21,13,14,
%T A119444 15,16,20,24,28,34,27,28,30,32,35,36,42,48,55,63,64,66,68,70,72,77,80,
%U A119444 81,89,109,110,111,112,115,120,126,128,135,140,144,207,208,210,212,215,216
%N A119444 Triangle as described in A100461, except with t(1,n) = Fibonacci(n+1).
%H A119444 G. C. Greubel, <a href="/A119444/b119444.txt">Table of n, a(n) for n = 1..1275</a>
%F A119444 Form an array t(m,n) (n >= 1, 1 <= m <= n) by: t(1,n) = Fibonacci(n+1) for all n; t(m+1,n) = (n-m)*floor( (t(m,n) - 1)/(n-m) ) for 1 <= m <= n-1.
%t A119444 t[n_, k_]:= t[n, k]= If[k==1, Fibonacci[n+1], (n-k+1)*Floor[(t[n, k-1] -1)/(n-k+1)]];
%t A119444 Table[t[n, n-k+1], {n,15}, {k,n}]//TableForm (* _G. C. Greubel_, Apr 07 2023 *)
%o A119444 (Magma)
%o A119444 function t(n,k)
%o A119444   if k eq 1 then return Fibonacci(n+1);
%o A119444   else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));
%o A119444   end if;
%o A119444 end function;
%o A119444 [t(n,n-k+1): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Apr 07 2023
%o A119444 (SageMath)
%o A119444 def t(n, k):
%o A119444     if (k==1): return fibonacci(n+1)
%o A119444     else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
%o A119444 flatten([[t(n, n-k+1) for k in range(1,n+1)] for n in range(1, 16)]) # _G. C. Greubel_, Apr 07 2023
%Y A119444 Cf. A119445 (leading diagonal).
%Y A119444 Cf. A100461 for powers of 2, A119446 for primes.
%K A119444 nonn,tabl
%O A119444 1,3
%A A119444 _Joshua Zucker_, May 20 2006