A178390 a(n) = (n^2 + 1)^2 + 1.

2, 5, 26, 101, 290, 677, 1370, 2501, 4226, 6725, 10202, 14885, 21026, 28901, 38810, 51077, 66050, 84101, 105626, 131045, 160802, 195365, 235226, 280901, 332930, 391877, 458330, 532901, 616226, 708965, 811802, 925445, 1050626, 1188101, 1338650, 1503077, 1682210

Offset

0,1

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

From Elmo R. Oliveira, Jun 05 2026: (Start)

G.f.: (2 - 5*x + 21*x^2 + x^3 + 5*x^4)/(1 - x)^5.

E.g.f.: (2 + x)*(1 + x + 4*x^2 + x^3)*exp(x).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

a(n) = A002522(n)^2 + 1 = A082044(n) + 1. (End)

Mathematica

Table[(n^2 + 1)^2 + 1, {n, 0, 5!}]

Crossrefs

Cf. A002522, A082044.

Sequence in context: A160048 A019047 A221679 * A045903 A090878 A214951

Adjacent sequences: A178387 A178388 A178389 * A178391 A178392 A178393

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, May 27 2010

Extensions

Offset changed to 0 by Georg Fischer, Mar 12 2020

More terms from Elmo R. Oliveira, Jun 05 2026

Status

approved