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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).

%I A047844 #23 Feb 03 2019 01:43:59
%S A047844 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,
%T A047844 97,127,127,19,32,52,82,125,181,237,237,23,40,68,112,179,276,403,530,
%U A047844 530,29,48,80,132,214,339,520,757,994,994,31,54,94,162,274
%N 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).
%H A047844 Nathaniel Johnston, <a href="/A047844/b047844.txt">Table of n, a(n) for n = 1..16653</a>
%e A047844 Array begins:
%e A047844   2,    3,    7,   13,   30,   56,  127,  237,  530, ...
%e A047844   3,    7,   13,   30,   56,  127,  237,  530,  994, ...
%e A047844   5,   10,   23,   43,   97,  181,  403,  757, 1662, ...
%e A047844   7,   16,   30,   67,  125,  276,  520, 1132, 2156, ...
%p A047844 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:
%p A047844 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
%t A047844 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 *)
%o A047844 (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))
%o A047844 for(s=2,9,for(k=1,s-1,print1(a(s-k,k)", "))) \\ _Charles R Greathouse IV_, Nov 26 2013
%Y A047844 Columns give A000040, A048448-A048455. See also A048456-A048466.
%K A047844 nonn,tabl,easy,nice
%O A047844 1,1
%A A047844 _N. J. A. Sloane_
%E A047844 a(46)-a(60) from _Nathaniel Johnston_, Apr 11 2011