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A051129
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Table T(n,k) = k^n read by antidiagonals (n >= 1, k >= 1).
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13
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1, 1, 2, 1, 4, 3, 1, 8, 9, 4, 1, 16, 27, 16, 5, 1, 32, 81, 64, 25, 6, 1, 64, 243, 256, 125, 36, 7, 1, 128, 729, 1024, 625, 216, 49, 8, 1, 256, 2187, 4096, 3125, 1296, 343, 64, 9, 1, 512, 6561, 16384, 15625, 7776, 2401, 512, 81, 10, 1, 1024, 19683, 65536, 78125
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OFFSET
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1,3
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COMMENTS
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(n-th term) = (n-th term of A002260)^(n-th term of A004736). Both A002260 and A004736 are related to A002024. - Robert A. Stump (bee_ess107(AT)yahoo.com), Aug 29 2002
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LINKS
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T. D. Noe, Rows n=1..50 of triangle, flattened
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FORMULA
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a(n) = (n - b(n) * (b(n) - 1) / 2)^(b(n) * (b(n) + 1) / 2 - n + 1), where b(n) = [ 1/2 + sqrt(2 * n) ]. (b(n) is the n-th term of A002024.) - Robert A. Stump (bee_ess107(AT)yahoo.com), Aug 29 2002
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EXAMPLE
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1 2 3 4 5 6 7
1 4 9 16 25 36 49
1 8 27 64 125 216 343
1 16 81 256 625 1296 2401
1 32 243 1024 3125 7776 16807
1 64 729 4096 15625 46656 117649
1 128 2187 16384 78125 279936 823543
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MATHEMATICA
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Table[ k^(n-k+1), {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 30 2012 *)
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PROG
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(Haskell)
a051129 n k = k ^ (n - k)
a051129_row n = a051129_tabl !! (n-1)
a051129_tabl = zipWith (zipWith (^)) a002260_tabl $ map reverse a002260_tabl
-- Reinhard Zumkeller, Sep 14 2014
(PARI) b(n) = floor(1/2 + sqrt(2 * n));
vector(100, n, (n - b(n) * (b(n) - 1) / 2)^(b(n) * (b(n) + 1) / 2 - n + 1)) \\ Altug Alkan, Dec 09 2015
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CROSSREFS
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Cf. A051128 (transposed), A003992 (transposed), A004248.
Cf. A002024, A002260, A004736.
Cf. A002260, A003101 (antidiagonal sums), A000169 (central terms), A003320 (row maxima), A247358 (sorted rows).
Sequence in context: A105851 A106195 A247023 * A319075 A264871 A067410
Adjacent sequences: A051126 A051127 A051128 * A051130 A051131 A051132
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from James A. Sellers, Dec 11 1999
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STATUS
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approved
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