A119445 Leading diagonal of triangle A119444.

1, 1, 1, 1, 1, 3, 7, 13, 27, 63, 109, 207, 331, 553, 931, 1531, 2527, 4093, 6673, 10831, 17563, 28561, 46227, 74883, 121219, 196239, 317607, 514047, 831823, 1346041, 2178079, 3524323, 5702619, 9227161, 14930019, 24157471, 39087823, 63245551

Offset: 1

Author

Joshua Zucker, May 20 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A119444 for triangle corresponding to this sequence.

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

Programs

Magma

function t(n,k) // t = A119444
  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): n in [1..60]]; // G. C. Greubel, Apr 07 2023

Mathematica

t[1, n_]:= Fibonacci[n+1];  (* t = A119444 *)
t[m_, n_]/; 1, ]= 0;
A119445[n_]:= A119445[n]= t[n,n];
Table[A119445[n], {n,60}] (* G. C. Greubel, Apr 07 2023 *)

SageMath

def t(n, k): # t = A119444
    if (k==1): return fibonacci(n+1)
    else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
def A119445(n): return t(n,n)
[A119445(n) for n in range(1,61)] # G. C. Greubel, Apr 07 2023

Formula

a(n) = A119444(n, n).