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| A317489
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Irregular triangle read by rows. For n >= 3 and 1 <= k <= floor(n/3), T(n,k) is the number of palindromic compositions of n into k parts of size at least 3.
(history;
published version)
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#26 by Bruno Berselli at Thu Sep 13 04:59:03 EDT 2018
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#25 by Jean-François Alcover at Thu Sep 13 04:56:16 EDT 2018
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#24 by Jean-François Alcover at Thu Sep 13 04:56:10 EDT 2018
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| MATHEMATICA
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T[n_, k_] := If[Mod[n, 2] == 1 && Mod[k, 2] == 0, 0, Binomial[Quotient[n-1, 2] - k, Quotient[k-1, 2]]];
Table[T[n, k], {n, 3, 30}, {k, 1, Quotient[n, 3]}] // Flatten (* Jean-François Alcover, Sep 13 2018, from PARI *)
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| STATUS
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approved
editing
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#23 by N. J. A. Sloane at Mon Sep 10 05:06:31 EDT 2018
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#22 by Christian Barrientos at Sat Sep 08 19:21:13 EDT 2018
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#21 by Christian Barrientos at Sat Sep 08 19:20:31 EDT 2018
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| NAME
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Irregular triangle read by rows. For n >= 3 and 1 <= k <= floor(n/3), T(n,k) is the number of symmetricpalindromic partitionscompositions of n into k parts of size at least 3 where order matters.
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| CROSSREFS
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Row sums of the triangle equal A226916(n+74).
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proposed
editing
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#20 by Jon E. Schoenfield at Fri Sep 07 23:09:36 EDT 2018
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#19 by Jon E. Schoenfield at Fri Sep 07 23:09:33 EDT 2018
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| NAME
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Irregular triangle read by rowrows. For n >= 3 and 1 <= k <= floor(n/3), T(n,k) is the number of symmetric partitions of n into k parts of size at least 3 where order matters.
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| STATUS
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proposed
editing
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#18 by Andrew Howroyd at Fri Sep 07 20:30:54 EDT 2018
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Discussion
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| Fri Sep 07
| 20:32
| Andrew Howroyd: I agree name should be palindromic compositions instead of symmetric partitions and then no need to state 'where order matters'
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| 20:35
| Andrew Howroyd: But it should be A226916(n+4) not n+7. (Don't forget this sequence starts at n=3)
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#17 by Andrew Howroyd at Fri Sep 07 20:25:53 EDT 2018
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| PROG
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(PARI) T(n, k)=if(n%2==1&&k%2==0, 0, binomial((n-1)\2-k, (k-1)\2)); \\ Andrew Howroyd, Sep 07 2018
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proposed
editing
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Discussion
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| Fri Sep 07
| 20:30
| Andrew Howroyd: A226916 is correct sequence for sums. Its a simple g.f and these are essentially sums of binomials. Also see Emeric Deutsh comment in A226916: number of palindromic compositions of n into {3,4,5,...} = A226916(n+4);
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