A176344 T(n,k) = 1 + A176343(n) - A176343(k) - A176343(n-k), triangle read by rows (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 11, 13, 11, 1, 1, 65, 75, 75, 65, 1, 1, 568, 632, 640, 632, 568, 1, 1, 7789, 8356, 8418, 8418, 8356, 7789, 1, 1, 168761, 176549, 177114, 177168, 177114, 176549, 168761, 1, 1, 5847568, 6016328, 6024114, 6024671, 6024671, 6024114, 6016328, 5847568, 1

Offset

0,8

Links

G. C. Greubel, Rows n = 0..75 of triangle, flattened

Example

Triangle begins:
  1;
  1,      1;
  1,      1,      1;
  1,      3,      3,      1;
  1,     11,     13,     11,      1;
  1,     65,     75,     75,     65,      1;
  1,    568,    632,    640,    632,    568,      1;
  1,   7789,   8356,   8418,   8418,   8356,   7789,      1;
  1, 168761, 176549, 177114, 177168, 177114, 176549, 168761, 1;
  ...

Maple

with(combinat);
b:= proc(n) option remember;
   if n = 0 then 0    else 1+fibonacci(n)*b(n-1)
   fi; end proc;
T:= proc (n, k) 1+b(n)-b(n-k)-b(k) end proc;
seq(seq(T(n, k), k = 0..n), n = 0..10); # G. C. Greubel, Dec 08 2019

Mathematica

b[n_]:= b[n]= If[n==0, 0, Fibonacci[n]*b[n-1] + 1]; (* A176343 *)
T[n_, k_]:= T[n, k] = 1 + a[n] - a[n-k] - a[k];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Dec 08 2019 *)

Prog

(Maxima) (a[0] : 0, a[n] := fib(n)*a[n-1] + 1, T(n, m) := 1 + a[n] - a[m] - a[n-m])$ create_list(T(n, m), n, 0, 10, m, 0, n); /* Franck Maminirina Ramaharo, Nov 25 2018 */
(PARI) b(n) = if(n==0, 0, 1 + fibonacci(n)*b(n-1) );
T(n, k) = 1 + b(n) - b(n-k) - b(k);
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Dec 07 2019
(Magma)
function b(n)
  if n eq 0 then return 0;
  else return 1 + Fibonacci(n)*b(n-1);
  end if; return b; end function;
function T(n, k) return 1 + b(n) - b(n-k) - b(k); end function; [ T(n, k) : k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 07 2019
(Sage)
def b(n):
    if (n==0): return 0
    else: return 1 + fibonacci(n)*b(n-1)
def T(n, k): return 1 + b(n) - b(n-k) - b(k)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 07 2019
(GAP)
b:= function(n)
    if n=0 then return 0;
    else return 1 + Fibonacci(n)*b(n-1);
    fi; end;
T:= function(n, k) return 1 + b(n) - b(n-k) - b(k); end;
Flat(List([0..10], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Dec 07 2019

Crossrefs

Cf. A156070, A156072, A176305, A176306, A176307, A176625, A176339.

Sequence in context: A172108 A220666 A104378 * A075837 A178885 A087107

Adjacent sequences: A176341 A176342 A176343 * A176345 A176346 A176347

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 15 2010

Extensions

Edited and name clarified by Franck Maminirina Ramaharo, Nov 25 2018

Status

approved