A226598 a(n) = c(n,n-1,...,1), the Cantor tuple function c applied to n-tuple (n,n-1,...,1).

0, 1, 7, 172, 159331, 457962302281, 34728196483190756583320206, 10559069708767287358379688495183368797732655643889529662

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10

Wikipedia, Pairing function

Formula

a(n) = c(n,n-1,...,1) 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.

Example

a(2) = c(2,1) = 3*4/2+1 = 7.
a(3) = c(3,2,1) = c(c(3,2),1) = c(5*6/2+2,1) = c(17,1) = 18*19/2+1 = 172.

Maple

c:= proc() `if`(nargs=0, 0,
           `if`(nargs=1, args,
           `if`(nargs=2, ((n, k)-> (s-> s*(s+1)/2)(n+k)+k)(args),
            c(c(args[1..-2]), args[-1]))))
    end:
a:= n-> c((n-i)$i=0..n-1):
seq(a(n), n=0..10);

Mathematica

c[args_List] := Switch[Length[args], 0, {0}, 1, args, 2, {Function[s, s*(s + 1)/2][#[[1]] + #[[2]]] + #[[2]]&[args]}, _, c[Append[c[args[[1 ;; -2]] ], args[[-1]]]]];
a[n_] := c[Table[(n - i), {i, 0, n - 1}]][[1]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, May 30 2018, from Maple *)

Crossrefs

Cf. A226588, A226597.

Sequence in context: A337676 A266306 A332117 * A075599 A012500 A220326

Adjacent sequences: A226595 A226596 A226597 * A226599 A226600 A226601

Keyword

nonn

Author

Alois P. Heinz, Jun 13 2013

Status

approved