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A117502 Triangle, row sums = A001595.

%I A117502 #16 Sep 08 2022 08:45:24
%S A117502 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,
%T A117502 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,
%U A117502 21,34,55,144,1,1,2,3,5,8,13,21,34,55,89,233
%N A117502 Triangle, row sums = A001595.
%C A117502 Row sums = A001595 = (1, 3, 9, 15, 25, 41, ...).
%H A117502 G. C. Greubel, <a href="/A117502/b117502.txt">Rows n = 1..100 of triangle, flattened</a>
%F A117502 n-th row = first n Fibonacci terms, with a deletion of F(n).
%F A117502 Columns of the triangle are difference terms of the array in A117501.
%F A117502 T(n,k) = Fibonacci(k) for k < n and T(n,n) = Fibonacci(n+1). - _G. C. Greubel_, Jul 10 2019
%e A117502 Row 5 of the triangle = (1, 1, 2, 3, 8); the first 5 Fibonacci terms with a deletion of F(5) = 5.
%e A117502 First few rows of the triangle are:
%e A117502   1;
%e A117502   1, 2;
%e A117502   1, 1, 3;
%e A117502   1, 1, 2, 5;
%e A117502   1, 1, 2, 3, 8; ...
%t A117502 Table[If[k==n, Fibonacci[n+1], Fibonacci[k]], {n, 20}, {k, n}]//Flatten (* _G. C. Greubel_, Jul 10 2019 *)
%o A117502 (PARI) T(n,k) = if(k==n, fibonacci(n+1), fibonacci(k)); \\ _G. C. Greubel_, Jul 10 2019
%o A117502 (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
%o A117502 (Sage)
%o A117502 def T(n, k):
%o A117502     if (k==n): return fibonacci(n+1)
%o A117502     else: return fibonacci(k)
%o A117502 [[T(n, k) for k in (1..n)] for n in (1..20)] # _G. C. Greubel_, Jul 10 2019
%o A117502 (GAP)
%o A117502 T:= function(n,k)
%o A117502     if k=n then return Fibonacci(n+1);
%o A117502     else return Fibonacci(k);
%o A117502     fi;
%o A117502   end;
%o A117502 Flat(List([1..20], n-> List([1..n], k-> T(n,k) ))); # _G. C. Greubel_, Jul 14 2019
%Y A117502 Cf. A000045, A117501, A001595.
%K A117502 nonn,tabl
%O A117502 1,3
%A A117502 _Gary W. Adamson_, Mar 23 2006
%E A117502 More terms added by _G. C. Greubel_, Jul 10 2019