cp's OEIS Frontend

A176270 Triangle T(n,m) = 1 + m*(m-n) read by rows, 0 <= m <= n.

%I A176270 #37 Sep 08 2022 08:45:52
%S A176270 1,1,1,1,0,1,1,-1,-1,1,1,-2,-3,-2,1,1,-3,-5,-5,-3,1,1,-4,-7,-8,-7,-4,
%T A176270 1,1,-5,-9,-11,-11,-9,-5,1,1,-6,-11,-14,-15,-14,-11,-6,1,1,-7,-13,-17,
%U A176270 -19,-19,-17,-13,-7,1,1,-8,-15,-20,-23,-24,-23,-20,-15,-8,1
%N A176270 Triangle T(n,m) = 1 + m*(m-n) read by rows, 0 <= m <= n.
%C A176270 For GCD(-1 - m,-1 - n + m) = 1, smallest number that cannot be written as a*(-1 - m) + b*(-1 - n + m) with a and b in the nonnegative integers. - _Thomas Anton_, May 22 2019
%H A176270 G. C. Greubel, <a href="/A176270/b176270.txt">Rows n = 0..100 of triangle, flattened</a>
%F A176270 T(n,m) = binomial(n-m+1,2) + binomial(m+1,2) - binomial(n+1,2) + 1 = m^2 - n*m + 1.
%F A176270 T(n,m) = T(n,n-m).
%F A176270 T(n,m) = 2 - A077028(n,m) for 0 <= m <= n. - _Werner Schulte_, Nov 10 2020
%e A176270 Triangle begins
%e A176270   1;
%e A176270   1,   1;
%e A176270   1,   0,   1;
%e A176270   1,  -1,  -1,   1;
%e A176270   1,  -2,  -3,  -2,   1;
%e A176270   1,  -3,  -5,  -5,  -3,   1;
%e A176270   1,  -4,  -7,  -8,  -7,  -4,   1;
%e A176270   1,  -5,  -9, -11, -11,  -9,  -5,   1;
%e A176270   1,  -6, -11, -14, -15, -14, -11,  -6,   1;
%e A176270   1,  -7, -13, -17, -19, -19, -17, -13,  -7,   1;
%e A176270   1,  -8, -15, -20, -23, -24, -23, -20, -15,  -8,   1;
%p A176270 A176270 := proc(n,m)
%p A176270         1+m*(m-n) ;
%p A176270 end proc: # _R. J. Mathar_, May 03 2013
%t A176270 Table[k*(k-n)+1, {n,0,12}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, May 30 2019 *)
%o A176270 (PARI) {T(n,k) = k*(k-n)+1}; \\ _G. C. Greubel_, May 30 2019
%o A176270 (Magma) [[k*(k-n)+1: k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, May 30 2019
%o A176270 (Sage) [[k*(k-n)+1 for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, May 30 2019
%o A176270 (GAP) Flat(List([0..12], n-> List([0..n], k-> k*(k-n)+1 ))); # _G. C. Greubel_, May 30 2019
%Y A176270 Cf. A005586 (row sums), A077028.
%K A176270 sign,tabl,easy
%O A176270 0,12
%A A176270 _Roger L. Bagula_, Apr 13 2010
%E A176270 Edited by _R. J. Mathar_, May 03 2013