cp's OEIS Frontend

A172176 Triangle T(n, k) = 1 + (n + k - n*k)*(2*n - k - n*(n-k)), read by rows.

%I A172176 #8 Apr 26 2022 04:22:16
%S A172176 1,2,2,1,2,1,-8,0,0,-8,-31,-4,5,-4,-31,-74,-10,22,22,-10,-74,-143,-18,
%T A172176 57,82,57,-18,-143,-244,-28,116,188,188,116,-28,-244,-383,-40,205,352,
%U A172176 401,352,205,-40,-383,-566,-54,330,586,714,714,586,330,-54,-566
%N A172176 Triangle T(n, k) = 1 + (n + k - n*k)*(2*n - k - n*(n-k)), read by rows.
%H A172176 G. C. Greubel, <a href="/A172176/b172176.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A172176 T(n, k) = 1 + (n-(n-1)*k)*(n-(n-1)*(n-k)).
%F A172176 T(n, n-k) = T(n, k).
%F A172176 T(n, 0) = 1 - A027620(n-3).
%F A172176 T(n, 1) = -A028552(n-3).
%F A172176 T(n, 2) = A033445(n-2).
%F A172176 Sum_{k=0..n} T(n, k) = (n+1)*(n^4 - 9*n^3 + 15*n^2 - n + 6)/6.
%e A172176 Triangle begins as:
%e A172176      1;
%e A172176      2,   2;
%e A172176      1,   2,   1;
%e A172176     -8,   0,   0,  -8;
%e A172176    -31,  -4,   5,  -4,  -31;
%e A172176    -74, -10,  22,  22,  -10,  -74;
%e A172176   -143, -18,  57,  82,   57,  -18, -143;
%e A172176   -244, -28, 116, 188,  188,  116,  -28, -244;
%e A172176   -383, -40, 205, 352,  401,  352,  205,  -40, -383;
%e A172176   -566, -54, 330, 586,  714,  714,  586,  330,  -54, -566;
%e A172176   -799, -70, 497, 902, 1145, 1226, 1145,  902,  497,  -70, -799;
%p A172176 A172176:= proc(n,m) 1+(n+m-n*m)*(2*n-m-n*(n-m)); end proc:
%p A172176 seq(seq(A172176(n,m), m=0..n), n=0..12);
%t A172176 T[n_, k_]= 1 + (n-(n-1)*k)*(n-(n-1)*(n-k));
%t A172176 Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten
%o A172176 (Magma) [1 + (n-(n-1)*k)*(n-(n-1)*(n-k)): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Apr 26 2022
%o A172176 (SageMath)
%o A172176 def A172176(n,k): return 1 + (n-(n-1)*k)*(n-(n-1)*(n-k))
%o A172176 flatten([[A172176(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Apr 26 2022
%Y A172176 Cf. A027620, A028552, A033445.
%K A172176 sign,tabl,easy
%O A172176 0,2
%A A172176 _Roger L. Bagula_, Jan 28 2010