A098152 a(n) = a(n-1)^2 + n, with a(0)=0.

0, 1, 3, 12, 148, 21909, 480004287, 230404115538378376, 53086056457022411804685755744397384, 2818129390158170901506703075470572449397357853477615482257305306043465

Offset: 0

Author

Henry Bottomley, Oct 25 2004

Keywords

• nonn

Examples

			a(4) = a(3)^2 + 4 =12^2 + 4 = 148.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..12
• Olivier Bodini, Danièle Gardy, Bernhard Gittenberger, Zbigniew Gołębiewski, On the number of unary-binary tree-like structures with restrictions on the unary height, arXiv:1510.01167 [math.CO], 2015, see Table 1, p. 19.
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A153058, A153059, A153060, A086851.

Programs

Magma

[0] cat [n eq 1 select 1 else Self(n-1)^2+n: n in [1..10]]; // Vincenzo Librandi, Oct 06 2015

Mathematica

a=0; lst={}; Do[a=a^2+n; AppendTo[lst, a], {n, 0, 11}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)
RecurrenceTable[{a[0]==0,a[n]==a[n-1]^2+n},a,{n,10}] (* Harvey P. Dale, Jul 28 2012 *)

Formula

For n>0, a(n) = floor(1.366609561487624975914833969579996...^(2^n)) = floor(A028300(n)^0.68178667449368682115305109818...) = ceiling(A003095(n)^1.53346965582393874689368175542252...).