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).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• easy
• nice

Examples

			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, ...
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..16653

Crossrefs

Columns give A000040, A048448-A048455. See also A048456-A048466.

Programs

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 *)

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

Extensions

a(46)-a(60) from Nathaniel Johnston, Apr 11 2011