A226201 a(n) = 8^n + n.

1, 9, 66, 515, 4100, 32773, 262150, 2097159, 16777224, 134217737, 1073741834, 8589934603, 68719476748, 549755813901, 4398046511118, 35184372088847, 281474976710672, 2251799813685265, 18014398509482002, 144115188075855891, 1152921504606846996, 9223372036854775829

Offset: 0

Author

Vincenzo Librandi, Jun 16 2013

Keywords

• nonn
• easy

Comments

Smallest prime of this form is a(101). - Bruno Berselli, Jun 17 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

Crossrefs

Cf. numbers of the form k^n+n: A006127 (k=2), A104743 (k=3), A158879 (k=4), A104745 (k=5), A226200 (k=6), A226199 (k=7), this sequence (k=8), A226202 (k=9), A081552 (k=10), A226737 (k=11).

Cf. A199555 (first differences).

Programs

Magma

[8^n+n: n in [0..30]];

Magma

I:=[1, 9, 66]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]];

Mathematica

Table[8^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(-1 + x + 7 x^2) / ((8 x - 1) (x - 1)^2), {x, 0, 30}], x]
LinearRecurrence[{10,-17,8},{1,9,66},30] (* Harvey P. Dale, Aug 11 2015 *)

PARI

a(n)=8^n+n \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (-1+x+7*x^2)/((8*x-1)*(x-1)^2).

a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).

E.g.f.: exp(x)*(exp(7*x) + x). - Elmo R. Oliveira, Mar 05 2025