A135378 Main diagonal of "square and add k" array.

2, 5, 38, 2707, 21418388, 3000279372337641, 255122481276683701099886061668842

Offset: 0

Author

Jonathan Vos Post, Dec 09 2007

Keywords

• easy
• nonn

Comments

Array of recurrence "start with 2, square and add k" begins:

k..|.A[k,n]=A[k,n-1]^2 + k

-1.|.2..3...8....63.......3968..15745023.247905749270528.............A003096

0..|.2..4..16...256......65536..4294967296.18446744073709551616......A001146

1..|.2..5..26...677.....458330..210066388901.44127887745906175987802.A003095

2..|.2..6..38..1446....2090918.4371938082726...19113842599189892819591078...

3..|.2..7..52..2707....7327852.53697414933907..2883412370584178505178284652.

4..|.2..8..68..4628...21418388.458747344518548.210449126102819371741916028308.

5..|.2..9..86..7401...54774806.3000279372337641.9001676312074749038996905444886.

6..|.2.10.106.11242..126382570.1597255405035792810...

7..|.2.11.128.16391..268664888.72180822044052551...

8..|.2.12.152.23112..534164552.285331768613360712..

9..|.2.13.178.31693.1004446258.1008912285210202573.

10.|.2.14.206.42446.1801662926.3245989298922881486.

Crossrefs

Cf. A001146, A003095, A003096, A062013.

Programs

Mathematica

A[k_,0] = 2; A[k_,n_] := A[k,n] = A[k, n-1]^2 + k; a[n_] := A[n, n]; a /@ Range[0, 6] (* Giovanni Resta, Jun 20 2016 *)

Formula

a(n) = A[n,n] where A[k,n] = n-th term of recurrence A[k,0] = 2, A[k,n] = A[k,n-1]^2 + k.

Extensions

Corrected and edited by Giovanni Resta, Jun 20 2016