A185097 a(1)=1; thereafter a(n+1) = T(8*a(n)), where T(i)=i*(i+1)/2 is the i-th triangular number.

1, 36, 41616, 55420693056, 98286503002057414584576, 309127573515950117423442905473334441338685531136

Offset: 1

Author

N. J. A. Sloane, Feb 18 2011

Keywords

• nonn

Comments

All terms are square and triangular; a subsequence of A001110.

References

• C. Alsina and R. B. Nelson, Charming Proofs: A Journey into Elegant Mathematics, MAA, 2010. See p. 4.

Crossrefs

Cf. A000217, A001110, A185096.

Programs

Maple

T:=n->n*(n+1)/2; t1:=[1]; for n from 1 to 7 do t1:= [op(t1), T(8*t1[nops(t1)])]; od: t1;

Mathematica

NestList[(8#(8#+1))/2&,1,7] (* Harvey P. Dale, Jan 20 2015 *)

Formula

a(n) = (1/8)*sinh(2^(n-2)*arccosh(17))^2. [Alexander R. Povolotsky, Aug 14 2011]

a(n+2) = 4*a(n+1)*(a(n+1)/(2*a(n))-1)^2, a(1)=1, a(2)=36. [Alexander R. Povolotsky, Aug 15 2011]

a(n) = A001110(2^(n-1)). - Ivan N. Ianakiev, Mar 11 2014