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A214661
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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.
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9
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1, 3, 9, 7, 15, 25, 13, 23, 35, 49, 21, 33, 47, 63, 81, 31, 45, 61, 79, 99, 121, 43, 59, 77, 97, 119, 143, 169, 57, 75, 95, 117, 141, 167, 195, 225, 73, 93, 115, 139, 165, 193, 223, 255, 289, 91, 113, 137, 163, 191, 221, 253, 287, 323, 361, 111, 135, 161, 189, 219, 251, 285, 321, 359, 399, 441
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OFFSET
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1,2
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LINKS
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FORMULA
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T(n, k) = (n+k)^2 - 3*n - k + 1.
T(2*n-1, n) = A214675() (main diagonal).
Sum_{k=1..n} T(n, k) = A051673(n) (row sums).
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EXAMPLE
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. Take the first n elements of the n-th diagonal (northwest to
. southeast) of the triangle on the left side
. and write this as n-th row on the triangle of the right side.
. 1: 1 1
. 2: 3 _ 3 9
. 3: 7 9 __ 7 15 25
. 4: 13 15 __ __ 13 23 35 49
. 5: 21 23 25 __ __ 21 33 47 63 ..
. 6: 31 33 35 __ __ __ 31 45 61 .. .. ..
. 7: 43 45 47 49 __ __ __ 43 59 .. .. .. .. ..
. 8: 57 59 61 63 __ __ __ __ 57 .. .. .. .. .. .. .. .
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MATHEMATICA
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Table[(n+k)^2-3*n-k+1, {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Mar 10 2024 *)
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PROG
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(Haskell)
import Data.List (transpose)
a214661 n k = a214661_tabl !! (n-1) !! (k-1)
a214661_row n = a214661_tabl !! (n-1)
a214661_tabl = zipWith take [1..] $ transpose $ map reverse a176271_tabl
(Magma) [(n+k)^2-3*n-k+1: k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 10 2024
(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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