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A132923 Triangle read by rows: T(n, k) = Fibonacci(k) + n - k.

%I A132923 #34 Mar 09 2025 13:45:08
%S A132923 1,2,1,3,2,2,4,3,3,3,5,4,4,4,5,6,5,5,5,6,8,7,6,6,6,7,9,13,8,7,7,7,8,
%T A132923 10,14,21,9,8,8,8,9,11,15,22,34,10,9,9,9,10,12,16,23,35,55,11,10,10,
%U A132923 10,11,13,17,24,36,56,89,12,11,11,11,12,14,18,25,37,57,90,144
%N A132923 Triangle read by rows: T(n, k) = Fibonacci(k) + n - k.
%C A132923 Row sums give A081662.
%C A132923 Right border is A000045.
%C A132923 Old name was: Triangle by columns, F(n) followed by (F(n)+1), (F(n)+2), (F(n)+3), ...
%H A132923 David A. Corneth, <a href="/A132923/b132923.txt">Table of n, a(n) for n = 1..10011</a>
%F A132923 T(k, k) = Fibonacci(k). T(k + n, k) = T(k, k) + n. - _David A. Corneth_, Feb 14 2023
%e A132923 First few rows of the triangle:
%e A132923   1;
%e A132923   2, 1;
%e A132923   3, 2, 2;
%e A132923   4, 3, 3, 3;
%e A132923   5, 4, 4, 4, 5;
%e A132923   6, 5, 5, 5, 6, 8;
%e A132923   7, 6, 6, 6, 7, 9, 13;
%e A132923   ...
%t A132923 T[n_,k_]:=n+Fibonacci[k]-k;Table[T[n,k],{n,12},{k,n}]//Flatten (* _James C. McMahon_, Mar 09 2025 *)
%o A132923 (PARI) T(n, k) = fibonacci(k) + n - k \\ _David A. Corneth_, Feb 14 2023
%Y A132923 Cf. A000045, A081662.
%K A132923 nonn,tabl
%O A132923 1,2
%A A132923 _Gary W. Adamson_, Sep 05 2007
%E A132923 More terms from and new name by _David A. Corneth_, Feb 14 2023