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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.
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2
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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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OFFSET
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1,22
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LINKS
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EXAMPLE
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Triangle begins:
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,
...
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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))):
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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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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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