A226588 - OEIS

%I #25 Jun 01 2018 09:17:57

%S 0,1,4,16,154,12091,73114279,2672849006516341,

%T 3572060905817699556013859788654,

%U 6379809557435582128907282471160505774257452233828787563248841

%N a(n) = c({1}^n), the Cantor tuple function c applied to an n-tuple of 1's.

%H Alois P. Heinz, <a href="/A226588/b226588.txt">Table of n, a(n) for n = 0..13</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pairing_function">Pairing function</a>

%F a(n) = c({1}^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.

%F a(n) = (a(n-1)+1)*(a(n-1)+2)/2+1 for n>1, a(n) = n for n<=1.

%e a(2) = c(1,1) = 2*3/2+1 = 4.

%e a(3) = c(1,1,1) = c(c(1,1),1) = c(4,1) = 5*6/2+1 = 16.

%p a:= proc(n) a(n):= `if`(n<2, n, (g-> g*(g+1)/2)(a(n-1)+1)+1) end:

%p seq(a(n), n=0..10);

%t a[n_] := a[n] = If[n<2, n, Function[g, g*(g+1)/2][a[n-1]+1]+1];

%t Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Jun 01 2018, from Maple *)

%Y Cf. A226597, A226598.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 12 2013