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%I #15 Mar 12 2024 09:53:45
%S 1,3,9,7,15,25,13,23,35,49,21,33,47,63,81,31,45,61,79,99,121,43,59,77,
%T 97,119,143,169,57,75,95,117,141,167,195,225,73,93,115,139,165,193,
%U 223,255,289,91,113,137,163,191,221,253,287,323,361,111,135,161,189,219,251,285,321,359,399,441
%N Odd numbers obtained by transposing the left half of A176271 into rows of a triangle: T(n,k) = A176271(n - 1 + k, k), 1 <= k <= n.
%H Reinhard Zumkeller, <a href="/A214661/b214661.txt">Rows n = 1..150 of triangle, flattened</a>
%F T(n, k) = (n+k)^2 - 3*n - k + 1.
%F T(n,k) = A176271(n+k-1, k).
%F T(n, k) = A214604(n,k) - 2*A025581(n,k).
%F T(n, k) = 2*A000290(A094727(n,k)) - A214604(n,k).
%F T(2*n-1, n) = A214675() (main diagonal).
%F T(n,1) = A002061(n).
%F T(n,n) = A016754(n-1).
%F Sum_{k=1..n} T(n, k) = A051673(n) (row sums).
%e . Take the first n elements of the n-th diagonal (northwest to
%e . southeast) 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: 3 _ 3 9
%e . 3: 7 9 __ 7 15 25
%e . 4: 13 15 __ __ 13 23 35 49
%e . 5: 21 23 25 __ __ 21 33 47 63 ..
%e . 6: 31 33 35 __ __ __ 31 45 61 .. .. ..
%e . 7: 43 45 47 49 __ __ __ 43 59 .. .. .. .. ..
%e . 8: 57 59 61 63 __ __ __ __ 57 .. .. .. .. .. .. .. .
%t Table[(n+k)^2-3*n-k+1, {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Mar 10 2024 *)
%o (Haskell)
%o import Data.List (transpose)
%o a214661 n k = a214661_tabl !! (n-1) !! (k-1)
%o a214661_row n = a214661_tabl !! (n-1)
%o a214661_tabl = zipWith take [1..] $ transpose $ map reverse a176271_tabl
%o (Magma) [(n+k)^2-3*n-k+1: k in [1..n], n in [1..15]]; // _G. C. Greubel_, Mar 10 2024
%o (SageMath) flatten([[(n+k)^2-3*n-k+1 for k in range(1,n+1)] for n in range(1,16)]) // _G. C. Greubel_, Mar 10 2024
%Y Cf. A000290, A002061, A016754, A025581, A094727, A176271, A214604.
%Y Cf. A051673 (row sums), A214675 (main diagonal).
%K nonn,tabl
%O 1,2
%A _Reinhard Zumkeller_, Jul 25 2012
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