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A132921 Triangle read by rows: T(n,k) = n + Fibonacci(k) - 1, 1 <= k <= n.

%I A132921 #11 Mar 09 2025 17:03:41
%S A132921 1,2,2,3,3,4,4,4,5,6,5,5,6,7,9,6,6,7,8,10,13,7,7,8,9,11,14,19,8,8,9,
%T A132921 10,12,15,20,28,9,9,10,11,13,16,21,29,42,10,10,11,12,14,17,22,30,43,
%U A132921 64,11,11,12,13,15,18,23,31,44,65,99,12,12,13,14,16,19,24,32,45,66,100,155
%N A132921 Triangle read by rows: T(n,k) = n + Fibonacci(k) - 1, 1 <= k <= n.
%C A132921 Right border = A081659, row sums = A132922: (1, 4, 10, 19, 32, ...).
%H A132921 Andrew Howroyd, <a href="/A132921/b132921.txt">Table of n, a(n) for n = 1..1275</a> (first 50 rows)
%F A132921 Equals (A127648 * A000012 + A000012 * A127647) - A000012 as infinite lower triangular matrices.
%e A132921 First few rows of the triangle are:
%e A132921   1;
%e A132921   2, 2;
%e A132921   3, 3, 4;
%e A132921   4, 4, 5, 6;
%e A132921   5, 5, 6, 7, 9;
%e A132921   ...
%e A132921 Column 3 = 4, 5, 6, 7, ...; since A081659(2) = 4.
%t A132921 T[n_,k_]:=n+Fibonacci[k]-1;Table[T[n,k],{n,12},{k,n}]//Flatten (* _James C. McMahon_, Mar 09 2025 *)
%o A132921 (PARI) T(n,k)=if(k<=n, n + fibonacci(k) - 1, 0) \\ _Andrew Howroyd_, Sep 01 2018
%Y A132921 Row sums are A132922.
%Y A132921 Cf. A127648, A127647, A081659.
%K A132921 nonn,tabl
%O A132921 1,2
%A A132921 _Gary W. Adamson_, Sep 05 2007
%E A132921 Name clarified and terms a(56) and beyond from _Andrew Howroyd_, Sep 01 2018