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%I #13 Mar 10 2024 09:35:56
%S 1,5,9,11,17,25,19,27,37,49,29,39,51,65,81,41,53,67,83,101,121,55,69,
%T 85,103,123,145,169,71,87,105,125,147,171,197,225,89,107,127,149,173,
%U 199,227,257,289,109,129,151,175,201,229,259,291,325,361,131,153,177,203,231,261,293,327,363,401,441
%N Odd numbers by transposing the right half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, n), 1 <= k <= n.
%H Reinhard Zumkeller, <a href="/A214604/b214604.txt">Rows n = 1..150 of triangle, flattened</a>
%F T(n,k) = (n+k)^2 - n - 3*k + 1.
%F Sum_{k=1..n} T(n, k) = A214659(n).
%F T(2*n-1, n) = A214660(n) (main diagonal).
%F T(n, 1) = A028387(n-1).
%F T(n, n) = A016754(n-1).
%F T(n, k) = A214661(n,k) + 2*A025581(n,k).
%F T(n, k) = 2*A000290(A094727(n,k)) - A214661(n,k).
%e . Take the first n elements of the n-th diagonal (northeast to
%e . southwest) of the triangle on the left side
%e . and write this as n-th row on the triangle of the right side.
%e . 1: 1 1
%e . 2: _ 5 5 9
%e . 3: _ 9 11 11 17 25
%e . 4: __ __ 17 19 19 27 37 49
%e . 5: __ __ 25 27 29 29 39 51 65 ..
%e . 6: __ __ __ 37 39 41 41 53 67 .. .. ..
%e . 7: __ __ __ 49 51 53 55 55 69 .. .. .. .. ..
%e . 8: __ __ __ __ 65 67 69 71 71 .. .. .. .. .. .. .. .
%t Table[(n+k)^2-n-3*k+1, {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Mar 10 2024 *)
%o (Haskell)
%o import Data.List (transpose)
%o a214604 n k = a214604_tabl !! (n-1) !! (k-1)
%o a214604_row n = a214604_tabl !! (n-1)
%o a214604_tabl = zipWith take [1..] $ transpose a176271_tabl
%o (Magma) [(n+k)^2-n-3*k+1: k in [1..n], n in [1..15]]; // _G. C. Greubel_, Mar 10 2024
%o (SageMath) flatten([[(n+k)^2-n-3*k+1 for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Mar 10 2024
%Y Cf. A000290, A016754, A028387, A025581, A094727, A176271.
%Y Cf. A214659 (row sums), A214660 (main diagonal), A214661.
%K nonn,tabl
%O 1,2
%A _Reinhard Zumkeller_, Jul 25 2012
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