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 A047844 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). 20
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..16653 EXAMPLE 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, ... MAPLE 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: for d from 1 to 8 do for m from 1 to d do print(A047844(d-m+1, m)):od:od: # Nathaniel Johnston, Apr 11 2011 MATHEMATICA 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 *) PROG (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)) for(s=2, 9, for(k=1, s-1, print1(a(s-k, k)", "))) \\ Charles R Greathouse IV, Nov 26 2013 CROSSREFS Columns give A000040, A048448-A048455. See also A048456-A048466. Sequence in context: A211890 A231406 A214034 * A081217 A320036 A053271 Adjacent sequences:  A047841 A047842 A047843 * A047845 A047846 A047847 KEYWORD nonn,tabl,easy,nice AUTHOR EXTENSIONS a(46)-a(60) from Nathaniel Johnston, Apr 11 2011 STATUS approved

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)