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A157454 Triangle read by rows: T(n, m) = min(2*m - 1, 2*(n - m) + 1).

%I A157454 #53 Jul 13 2025 19:06:47
%S A157454 1,1,1,1,3,1,1,3,3,1,1,3,5,3,1,1,3,5,5,3,1,1,3,5,7,5,3,1,1,3,5,7,7,5,
%T A157454 3,1,1,3,5,7,9,7,5,3,1,1,3,5,7,9,9,7,5,3,1,1,3,5,7,9,11,9,7,5,3,1
%N A157454 Triangle read by rows: T(n, m) = min(2*m - 1, 2*(n - m) + 1).
%H A157454 Reinhard Zumkeller, <a href="/A157454/b157454.txt">Rows n = 1..125 of triangle, flattened</a>
%F A157454 T(n,m) = T(n,n-m) = 2*m-1 for 0 <= m <= n/2, otherwise 2*(n-m)+1.
%F A157454 a(n) = 2*A003983(n) - 1.
%F A157454 From _Ridouane Oudra_, Jul 20 2019: (Start)
%F A157454 a(n) = A002024(n) - A049581(n-1).
%F A157454 a(n) = t - abs(t^2-2n+1), where t = floor(sqrt(2n)+1/2). (End)
%e A157454 Triangle starts:
%e A157454   1;
%e A157454   1,  1;
%e A157454   1,  3,  1;
%e A157454   1,  3,  3,  1;
%e A157454   1,  3,  5,  3,  1;
%e A157454   1,  3,  5,  5,  3,  1;
%e A157454   1,  3,  5,  7,  5,  3,  1;
%e A157454   1,  3,  5,  7,  7,  5,  3,  1;
%e A157454   1,  3,  5,  7,  9,  7,  5,  3,  1;
%e A157454   1,  3,  5,  7,  9,  9,  7,  5,  3,  1;
%e A157454   1,  3,  5,  7,  9, 11,  9,  7,  5,  3,  1;
%e A157454   ...
%t A157454 Table[Min[2*k-1, 2*(n-k)+1], {n,1,12}, {k,1,n}]//Flatten (* modified by _G. C. Greubel_, Jun 30 2019 *)
%o A157454 (Haskell)
%o A157454 import Data.List (inits)
%o A157454 a157454 n k = a157454_tabl !! (n-1) !! (k-1)
%o A157454 a157454_row n = a157454_tabl !! (n-1)
%o A157454 a157454_tabl = concatMap h $ tail $ inits [1, 3 ..] where
%o A157454    h xs = [xs ++ tail xs', xs ++ xs'] where xs' = reverse xs
%o A157454 -- _Reinhard Zumkeller_, Dec 15 2013
%o A157454 (PARI) {T(n,k) = min(2*k-1, 2*(n-k)+1)};
%o A157454 for(n=1,12, for(k=1,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Jun 30 2019
%o A157454 (Magma) [[Min(2*k-1, 2*(n-k)+1): k in [1..n]]: n in [1..12]]; // _G. C. Greubel_, Jun 30 2019
%o A157454 (Sage) [[min(2*k-1, 2*(n-k)+1) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, Jun 30 2019
%o A157454 (GAP) Flat(List([1..12], n-> List([1..n], k-> Minimum(2*k-1, 2*(n-k)+1) ))); # _G. C. Greubel_, Jun 30 2019
%o A157454 (Python)
%o A157454 from math import isqrt
%o A157454 def A157454(n): return (isqrt(n<<3)+1>>1)-abs((k:=n<<1)-((m:=isqrt(k))+(k>m*(m+1)))**2-1) # _Chai Wah Wu_, Jun 08 2025
%Y A157454 Cf. A003983, A005408.
%Y A157454 Row sums are A000982(n).
%K A157454 nonn,easy,tabl
%O A157454 1,5
%A A157454 _Roger L. Bagula_, Mar 01 2009
%E A157454 Edited by the Associate Editors of the OEIS, Apr 10 2009