A115410 Sequence of iterated sums of squares (1^2+2^2+3^2+...+n^2).

1, 55, 349074740, 7458911738724515315524082613205180, 159232823342755035454279356693126603659457648808279391910878167820461916066223383414616137125812767424153893199341493609630

Offset

1,2

Comments

Can be understood as generalized iterated square pyramidal numbers. The growth of the sequence is bounded by O(n^3^n/3^(n/2)). This can be derived from the growth O(n^3/3) of the power two sum (1^2+2^2+3^2+...+n^2) by iteration.

Links

Table of n, a(n) for n=1..5.

Formula

Let T(n):=Sum_{k=1..n} k^2; we define a(1):=T(1), a(2):=T(T(2)) etc., a(n):=T(T(T(...T(n))...))).

Example

a(2)=T(T(2))=T(5)=55;
a(3)=T(T(T(3)))=T(T(14))=T(1015)=349074740.

Mathematica

t[n_]:=Sum[k^2, {k, n}]; Table[Nest[t[#]&, n, n], {n, 5}] (* James C. McMahon, Aug 10 2024 *)

Crossrefs

Cf. A000330, A099129.

Sequence in context: A093255 A172896 A201823 * A250489 A308097 A172533

Adjacent sequences: A115407 A115408 A115409 * A115411 A115412 A115413

Keyword

nonn,easy

Author

Hieronymus Fischer, Jan 22 2006

Status

approved