The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A309148 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A309148

A(n,k) is (1/k) times the number of n-member subsets of [k*n] whose elements sum to a multiple of n; square array A(n,k), n>=1, k>=1, read by antidiagonals.
(history; published version)

#29 by N. J. A. Sloane at Fri Oct 04 13:10:05 EDT 2019

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proposed

approved

#28 by Jean-François Alcover at Fri Oct 04 12:38:34 EDT 2019

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editing

proposed

#27 by Jean-François Alcover at Fri Oct 04 12:38:29 EDT 2019

MATHEMATICA

A[n_, k_] := 1/(n k) Sum[Binomial[k d, d] (-1)^(n+d) EulerPhi[n/d], {d, Divisors[n]}];

Table[A[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Oct 04 2019 *)

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approved

editing

#26 by Alois P. Heinz at Tue Jul 16 12:15:40 EDT 2019

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editing

approved

#25 by Alois P. Heinz at Mon Jul 15 18:12:00 EDT 2019

CROSSREFS

Columns k=1-2 10 give: A000035, A145855, A309182, A309183, A309184, A309185, A309186, A309187, A309188, A309189.

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approved

editing

#24 by Alois P. Heinz at Sun Jul 14 15:45:11 EDT 2019

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editing

approved

#23 by Alois P. Heinz at Sun Jul 14 15:45:08 EDT 2019

FORMULA

A(n,k) = 1/(n*k) * Sum_{d|n} binomial(k*d,d)*(-1)^(n+d)*phi(n/d).

#22 by Alois P. Heinz at Sun Jul 14 15:41:37 EDT 2019

CROSSREFS

Cf. A000010, A304482.

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approved

editing

#21 by Alois P. Heinz at Sun Jul 14 15:09:26 EDT 2019

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editing

approved

#20 by Alois P. Heinz at Sun Jul 14 15:09:22 EDT 2019

EXAMPLE

Square array A(n,k) begins:

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approved

editing