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%I #17 Apr 05 2023 09:34:45
%S 1,1,1,2,0,1,3,0,0,1,4,0,0,0,1,5,0,0,0,0,1,6,0,0,0,0,0,1,7,0,0,0,0,0,
%T 0,1,8,0,0,0,0,0,0,0,1,9,0,0,0,0,0,0,0,0,1,10,0,0,0,0,0,0,0,0,0,1,11,
%U 0,0,0,0,0,0,0,0,0,0,1,12,0,0,0,0,0,0,0,0,0,0,0,1,13,0,0,0,0,0,0,0,0,0,0,0,0,1
%N Triangle read by rows: row n (n>=0) ends with 1, and for n>=1 begins with n; other entries are zero.
%H G. C. Greubel, <a href="/A158821/b158821.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = A145677(n, n-k-1). - _R. J. Mathar_, Apr 01 2009
%F From _G. C. Greubel_, Dec 22 2021: (Start)
%F Sum_{k=0..n} T(n, k) = A000027(n).
%F Sum_{k=0..floor(n/2)} T(n-k, k) = A109613(n). (End)
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 0, 1;
%e 3, 0, 0, 1;
%e 4, 0, 0, 0, 1;
%e 5, 0, 0, 0, 0, 1;
%e 6, 0, 0, 0, 0, 0, 1;
%e 7, 0, 0, 0, 0, 0, 0, 1;
%p A158821:= proc(n,k)
%p if n = k then 1;
%p elif k = 0 then n;
%p else 0;
%p end if;
%p end proc: # _R. J. Mathar_, Jan 08 2015
%t T[n_, k_]:= If[k==0, Boole[n==0] +n, If[k==n, 1, 0]];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Dec 22 2021 *)
%t Join[{1},Table[Join[{n},PadLeft[{1},n,0]],{n,15}]]//Flatten (* _Harvey P. Dale_, Apr 05 2023 *)
%o (Sage)
%o def A158821(n,k):
%o if (k==0): return n + bool(n==0)
%o elif (k==n): return 1
%o else: return 0
%o flatten([[A158821(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Dec 22 2021
%Y Cf. A000027, A109613, A145677.
%K nonn,tabl,easy
%O 0,4
%A _Gary W. Adamson_, Mar 30 2008
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