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
Examples
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; ...
Links
- G. C. Greubel, Rows n = 0..75 of triangle, flattened
Programs
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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 -
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
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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
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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 *)
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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 */
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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
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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
Extensions
Edited and name clarified by Franck Maminirina Ramaharo, Nov 25 2018