A226597 a(n) = c(1,2,...,n), the Cantor tuple function c applied to n-tuple (1,2,...,n).

0, 1, 8, 69, 2705, 3673410, 6746994391242, 22760966657776105541085632, 259030801598197790167764376907440725907087677647628

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

Cf. A226588, A226598.

Sequence in context: A327606 A336951 A335114 * A376855 A209074 A124152

Adjacent sequences: A226594 A226595 A226596 * A226598 A226599 A226600

Keyword

nonn

Author

Alois P. Heinz, Jun 13 2013

Status

approved