OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..12
Wikipedia, Pairing function
FORMULA
a(n) = c(1,2,...,n) with c() = 0, c(n) = n, c(n,k) = (n+k)*(n+k+1)/2+k, c(n_1,...,n_{k-1},n_k) = c(c(n_1,...,n_{k-1}),n_k) for k>2.
a(n) = (a(n-1)+n)*(a(n-1)+n+1)/2+n for n>1, a(n) = n for n<=1.
EXAMPLE
a(2) = c(1,2) = 3*4/2+2 = 8.
a(3) = c(1,2,3) = c(c(1,2),3) = c(8,3) = 11*12/2+3 = 69.
MAPLE
a:= proc(n) a(n):= `if`(n<2, n, (g-> g*(g+1)/2)(a(n-1)+n)+n) end:
seq(a(n), n=0..10);
MATHEMATICA
a[n_] := a[n] = If[n < 2, n, Function[g, g*(g + 1)/2][a[n - 1] + n] + n] ;
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, May 30 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 13 2013
STATUS
approved