A015489 a(0)=1, a(1)=4, a(n) = Sum_{k=0..n-1} 4^k*a(k).

1, 4, 17, 289, 18785, 4827745, 4948438625, 20273753046625, 332185443668950625, 21770437421732017110625, 5707011317919939625464790625, 5984240806710536532650993759190625, 25099731136790036931580726379142034390625, 421103635923583133039143999480490184792978390625

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = (4^(n-1) + 1) * a(n-1) for n >= 3. - Vincenzo Librandi, Nov 11 2012

From Vaclav Kotesovec, Nov 06 2025: (Start)

For n > 1, a(n) = 17*QPochhammer(-1, 4, n)/10.

a(n) ~ 17*QPochhammer(-1/4, 1/4) * 2^(n*(n-1)) / 5. (End)

Mathematica

Join[{0, 1}, Table[17*QPochhammer[-1, 4, n]/10, {n, 2, 15}]] (* Vaclav Kotesovec, Nov 06 2025 *)

Prog

(Magma) I:=[1, 4, 17]; [n le 3 select I[n] else (4^(n-2)+1)*Self(n-1): n in [1..15]]; // Vincenzo Librandi, Nov 11 2012

Crossrefs

Sequence in context: A214143 A320986 A302145 * A153061 A277762 A337477

Adjacent sequences: A015486 A015487 A015488 * A015490 A015491 A015492

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Jason Yuen, Nov 06 2025

Status

approved