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

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, 15, 16, 20, 24, 28, 34, 27, 28, 30, 32, 35, 36, 42, 48, 55, 63, 64, 66, 68, 70, 72, 77, 80, 81, 89, 109, 110, 111, 112, 115, 120, 126, 128, 135, 140, 144, 207, 208, 210, 212, 215, 216

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1275

Formula

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.

Mathematica

t[n_, k_]:= t[n, k]= If[k==1, Fibonacci[n+1], (n-k+1)*Floor[(t[n, k-1] -1)/(n-k+1)]];
Table[t[n, n-k+1], {n, 15}, {k, n}]//TableForm (* G. C. Greubel, Apr 07 2023 *)

Prog

(Magma)
function t(n, k)
  if k eq 1 then return Fibonacci(n+1);
  else return (n-k+1)*Floor((t(n, k-1) -1)/(n-k+1));
  end if;
end function;
[t(n, n-k+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Apr 07 2023
(SageMath)
def t(n, k):
    if (k==1): return fibonacci(n+1)
    else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
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

Crossrefs

Cf. A119445 (leading diagonal).

Cf. A100461 for powers of 2, A119446 for primes.

Sequence in context: A238954 A238967 A066657 * A060040 A092080 A264482

Adjacent sequences: A119441 A119442 A119443 * A119445 A119446 A119447

Keyword

nonn,tabl

Author

Joshua Zucker, May 20 2006

Status

approved