Revision History for A261013
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Showing entries 1-10
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| A261013
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Irregular triangle read by rows: T(n,k) = number of partitions of n into prime parts in which the largest part is the k-th prime.
(history;
published version)
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#16 by Bruno Berselli at Tue Dec 06 10:58:04 EST 2016
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#15 by Jean-François Alcover at Tue Dec 06 09:58:29 EST 2016
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#14 by Jean-François Alcover at Tue Dec 06 09:58:23 EST 2016
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| MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i-1] + Function[p, If[p>n, 0, b[n-p, i]]][Prime[i]]]]; T[n_] := If[n == 1, 0, Table[b[n - Prime[k], k], {k, 1, PrimePi[n]}]]; Table[T[n], {n, 1, 25}] // Flatten (* Jean-François Alcover, Dec 06 2016 after Alois P. Heinz *)
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approved
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#13 by Alois P. Heinz at Sun Aug 16 19:32:32 EDT 2015
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#12 by Alois P. Heinz at Sun Aug 16 19:32:26 EDT 2015
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| DATA
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0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 2, 1, 0, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 2, 3, 2, 1, 1, 1, 2, 3, 3, 1, 0, 0, 3, 4, 3, 1, 1, 1, 2, 4, 4, 2, 1, 0, 3, 5, 5, 2, 1, 1, 1, 3, 5, 5, 3, 2, 0, 0, 3, 6, 7, 3, 2, 1, 1, 1, 3, 7, 7, 4, 3, 1, 0
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approved
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#11 by Alois P. Heinz at Sun Aug 16 19:30:49 EDT 2015
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#10 by Alois P. Heinz at Sun Aug 16 19:30:46 EDT 2015
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| KEYWORD
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nonn,tabf,look,new
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approved
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#9 by Alois P. Heinz at Sun Aug 16 19:29:48 EDT 2015
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#8 by Alois P. Heinz at Sun Aug 16 19:29:44 EDT 2015
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| LINKS
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Alois P. Heinz, <a href="/A261013/b261013.txt">Rows n = 1..500, flattened</a>
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| MAPLE
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with(numtheory):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+(p-> `if`(p>n, 0, b(n-p, i)))(ithprime(i))))
end:
T:= n-> `if`(n=1, 0, seq(b(n-ithprime(k), k), k=1..pi(n))):
seq(T(n), n=1..25); # Alois P. Heinz, Aug 16 2015
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#7 by Alois P. Heinz at Sun Aug 16 19:25:11 EDT 2015
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| DATA
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0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 2, 1, 0, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 2, 3, 2, 1, 1, 1, 2, 3, 3, 1, 0, 0, 3, 4, 3, 1, 1, 1, 2, 4, 4, 2, 1, 0, 3, 5, 5, 2, 1, 1, 1, 3, 5, 5, 3, 2, 0, 0, 3, 6, 7, 3, 2, 1, 1
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| OFFSET
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1,2122
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| KEYWORD
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nonn,tabf,more,new
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| EXTENSIONS
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More terms from Alois P. Heinz, Aug 16 2015
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