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A047844
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Patrick De Geest's "Generations" array read by antidiagonals: a(n,1) = n-th prime, a(1,k+1) = a(2,k), a(n,k+1) = a(n-1,k) + a(n+1,k).
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20
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2, 3, 3, 5, 7, 7, 7, 10, 13, 13, 11, 16, 23, 30, 30, 13, 20, 30, 43, 56, 56, 17, 28, 44, 67, 97, 127, 127, 19, 32, 52, 82, 125, 181, 237, 237, 23, 40, 68, 112, 179, 276, 403, 530, 530, 29, 48, 80, 132, 214, 339, 520, 757, 994, 994, 31, 54, 94, 162, 274
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OFFSET
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1,1
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LINKS
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EXAMPLE
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Array begins:
2, 3, 7, 13, 30, 56, 127, 237, 530, ...
3, 7, 13, 30, 56, 127, 237, 530, 994, ...
5, 10, 23, 43, 97, 181, 403, 757, 1662, ...
7, 16, 30, 67, 125, 276, 520, 1132, 2156, ...
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MAPLE
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A047844:=proc(n, k)global a:if(type(a[n, k], integer))then return a[n, k]:elif(k=1)then a[n, k]:=ithprime(n):elif(n=1)then a[n, k]:=A047844(2, k-1):else a[n, k]:=A047844(n-1, k-1)+A047844(n+1, k-1):fi:return a[n, k]:end:
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MATHEMATICA
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a[n_, 1] := a[n, 1] = Prime[n]; a[1, k_] := a[1, k] = a[2, k-1]; a[n_, k_] := a[n, k] = a[n-1, k-1] + a[n+1, k-1]; Table[a[n-k+1, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 26 2013 *)
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PROG
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(PARI) a(n, k)=if(k==1, prime(n), n==1, a(2, k-1), a(n-1, k-1)+a(n+1, k-1))
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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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