login
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
OFFSET
1,1
LINKS
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: A231406 A214034 A343224 * A081217 A335139 A320036
KEYWORD
nonn,tabl,easy,nice
EXTENSIONS
a(46)-a(60) from Nathaniel Johnston, Apr 11 2011
STATUS
approved

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy