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Revision History for A282011

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A282011

Number T(n,k) of k-element subsets of [n] having an even sum; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
(history; published version)

#42 by Alois P. Heinz at Thu Aug 02 18:55:22 EDT 2018

STATUS

editing

approved

#41 by Alois P. Heinz at Thu Aug 02 18:55:20 EDT 2018

EXAMPLE

1;

1, 0;

1, 1, 0;

1, 1, 1, 1;

1, 2, 2, 2, 1;

1, 2, 4, 6, 3, 0;

1, 3, 6, 10, 9, 3, 0;

1, 3, 9, 19, 19, 9, 3, 1;

1, 4, 12, 28, 38, 28, 12, 4, 1;

1, 4, 16, 44, 66, 60, 40, 20, 5, 0;

1, 5, 20, 60, 110, 126, 100, 60, 25, 5, 0;

1, 5, 25, 85, 170, 226, 226, 170, 85, 25, 5, 1;

1, 6, 30, 110, 255, 396, 452, 396, 255, 110, 30, 6, 1;

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approved

editing

#40 by Alois P. Heinz at Tue Jul 31 16:47:11 EDT 2018

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editing

approved

#39 by Alois P. Heinz at Tue Jul 31 16:46:20 EDT 2018

FORMULA

Sum_{k=0..n} (k+1) * T(n,k) = A087447(n) + [n=2].

CROSSREFS

Cf. A007318, A057711, A087447, A159916.

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approved

editing

#38 by Alois P. Heinz at Tue Jul 31 16:40:44 EDT 2018

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editing

approved

#37 by Alois P. Heinz at Tue Jul 31 16:39:54 EDT 2018

FORMULA

Sum_{k=0..n} k * T(n,k) = A057711(n-1) for n>0.

CROSSREFS

Cf. A007318, A057711, A159916.

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approved

editing

#36 by Alois P. Heinz at Tue Jul 31 16:05:19 EDT 2018

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approved

#35 by Alois P. Heinz at Tue Jul 31 16:05:15 EDT 2018

LINKS

Johann Cigler, <a href="https://homepage.univie.ac.at/johann.cigler/preprints/losanitsch3.pdf">Some Pascal-like triangles</a>, 2018.

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approved

editing

#34 by Bruno Berselli at Thu Nov 16 06:19:22 EST 2017

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proposed

approved

#33 by Michel Marcus at Thu Nov 16 05:45:55 EST 2017

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editing

proposed

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Last modified August 19 03:14 EDT 2024. Contains 375284 sequences. (Running on oeis4.)