A117502 Triangle, row sums = A001595.

1, 1, 2, 1, 1, 3, 1, 1, 2, 5, 1, 1, 2, 3, 8, 1, 1, 2, 3, 5, 13, 1, 1, 2, 3, 5, 8, 21, 1, 1, 2, 3, 5, 8, 13, 34, 1, 1, 2, 3, 5, 8, 13, 21, 55, 1, 1, 2, 3, 5, 8, 13, 21, 34, 89, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 144, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 233

Offset: 1

Author

Gary W. Adamson, Mar 23 2006

Keywords

• nonn
• tabl

Comments

Row sums = A001595 = (1, 3, 9, 15, 25, 41, ...).

Examples

			Row 5 of the triangle = (1, 1, 2, 3, 8); the first 5 Fibonacci terms with a deletion of F(5) = 5.
First few rows of the triangle are:
  1;
  1, 2;
  1, 1, 3;
  1, 1, 2, 5;
  1, 1, 2, 3, 8; ...
		

Links

• G. C. Greubel, Rows n = 1..100 of triangle, flattened

Crossrefs

Cf. A000045, A117501, A001595.

Programs

GAP

T:= function(n,k)
    if k=n then return Fibonacci(n+1);
    else return Fibonacci(k);
    fi;
  end;
Flat(List([1..20], n-> List([1..n], k-> T(n,k) ))); # G. C. Greubel, Jul 14 2019

Magma

[k eq n select Fibonacci(n+1) else Fibonacci(k): k in [1..n], n in [1..20]]; // G. C. Greubel, Jul 10 2019

Mathematica

Table[If[k==n, Fibonacci[n+1], Fibonacci[k]], {n, 20}, {k, n}]//Flatten (* G. C. Greubel, Jul 10 2019 *)

PARI

T(n,k) = if(k==n, fibonacci(n+1), fibonacci(k)); \\ G. C. Greubel, Jul 10 2019

Sage

def T(n, k):
    if (k==n): return fibonacci(n+1)
    else: return fibonacci(k)
[[T(n, k) for k in (1..n)] for n in (1..20)] # G. C. Greubel, Jul 10 2019

Formula

n-th row = first n Fibonacci terms, with a deletion of F(n).

Columns of the triangle are difference terms of the array in A117501.

T(n,k) = Fibonacci(k) for k < n and T(n,n) = Fibonacci(n+1). - G. C. Greubel, Jul 10 2019

Extensions

More terms added by G. C. Greubel, Jul 10 2019