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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-Fran├žois 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 A053271 A035360

Adjacent sequences:  A047841 A047842 A047843 * A047845 A047846 A047847

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified March 28 05:07 EDT 2017. Contains 284182 sequences.