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A129705 Triangle T(n,m) = A000071(n+2)-m*(m+1)/2 read by rows.

%I A129705 #11 Feb 16 2025 08:33:05
%S A129705 0,1,0,2,1,-1,4,3,1,-2,7,6,4,1,-3,12,11,9,6,2,-3,20,19,17,14,10,5,-1,
%T A129705 33,32,30,27,23,18,12,5,54,53,51,48,44,39,33,26,18,88,87,85,82,78,73,
%U A129705 67,60,52,43,143,142,140,137,133,128,122,115,107,98,88
%N A129705 Triangle T(n,m) = A000071(n+2)-m*(m+1)/2 read by rows.
%C A129705 The row sums are 0, 1, 2, 6, 15, 37, 84, 180, 366, 715, 1353, 2498, 4524 = (n+1)*(A000071(n+2) -(n+2)*n/6). - _R. J. Mathar_, Sep 09 2011
%H A129705 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SchubertVariety.html">Schubert Variety</a>
%F A129705 t(n,m) = sum_{i=0..n} A000045(i) - sum_{i=0..m} i, 0<=m<=n.
%e A129705 0;
%e A129705 1, 0;
%e A129705 2, 1, -1;
%e A129705 4, 3, 1, -2;
%e A129705 7, 6, 4, 1, -3;
%e A129705 12, 11, 9, 6, 2, -3;
%e A129705 20, 19, 17, 14, 10, 5, -1;
%e A129705 33, 32, 30, 27, 23, 18, 12, 5;
%p A129705 A000071 := proc(n) if n = 0 then 0; else combinat[fibonacci](n)-1 ; end if; end proc:
%p A129705 A129705 := proc(n,m) A000071(n+2)-m*(m+1)/2 ; end proc: # _R. J. Mathar_, Sep 09 2011
%t A129705 fib[n_Integer?Positive] := fib[n] = fib[n - 1] + fib[n - 2]; fib[0] = 0; fib[1] = fib[2] = 1; t[n_, m_] = Sum[fib[i], {i, 0, n}] - Sum[i, {i, 0, m}]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
%Y A129705 Cf. A000045.
%K A129705 tabl,easy,sign
%O A129705 0,4
%A A129705 _Roger L. Bagula_, Jun 08 2007