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%I #26 Oct 01 2023 16:34:02
%S 1,1,1,1,0,1,1,1,1,1,1,2,2,2,1,1,3,4,4,3,1,1,4,1,2,1,4,1,1,5,5,3,3,5,
%T 5,1,1,6,2,0,6,0,2,6,1,1,7,8,2,6,6,2,8,7,1,1,8,5,0,8,2,8,0,5,8,1,1,9,
%U 2,5,8,10,10,8,5,2,9,1,1,10,11,7,1,6,8,6
%N Rows of triangle formed using Pascal's rule, except sums in the n-th row are modulo n: T(n,0) = T(n,n) = 1 and T(n,k) = (T(n-1,k-1) + T(n-1,k)) mod n.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 0, 1;
%e 1, 1, 1, 1;
%e 1, 2, 2, 2, 1;
%e 1, 3, 4, 4, 3, 1;
%e 1, 4, 1, 2, 1, 4, 1;
%e 1, 5, 5, 3, 3, 5, 5, 1;
%e 1, 6, 2, 0, 6, 0, 2, 6, 1;
%e 1, 7, 8, 2, 6, 6, 2, 8, 7, 1;
%e 1, 8, 5, 0, 8, 2, 8, 0, 5, 8, 1;
%e 1, 9, 2, 5, 8, 10, 10, 8, 5, 2, 9, 1;
%t T[n_,k_]:=If[k==0 || k==n, 1, Mod[T[n - 1, k - 1] + T[n- 1, k], n]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* _Indranil Ghosh_, Apr 29 2017 *)
%o (Python)
%o src = [0]*1024
%o dst = [0]*1024
%o for n in range(19):
%o dst[0] = dst[n] = 1
%o for k in range(1, n):
%o dst[k] = (src[k-1]+src[k]) % n
%o for k in range(n+1):
%o src[k] = dst[k]
%o print(dst[k], end=',')
%Y Cf. A007318 - Pascal's triangle read by rows.
%Y Cf. A047999, A083093, A034931, A034930, A034932, A008975.
%K nonn,tabl
%O 0,12
%A _Alex Ratushnyak_, Jun 06 2012
%E Offset corrected by _Joerg Arndt_, Dec 05 2016
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