A226737 a(n) = 11^n + n.

1, 12, 123, 1334, 14645, 161056, 1771567, 19487178, 214358889, 2357947700, 25937424611, 285311670622, 3138428376733, 34522712143944, 379749833583255, 4177248169415666, 45949729863572177, 505447028499293788, 5559917313492231499, 61159090448414546310, 672749994932560009221

Offset: 0

Author

Vincenzo Librandi, Jun 16 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (13,-23,11).

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), A226201 (k=8), A226202 (k=9), A081552 (k=10), this sequence (k=11).

Cf. A199764 (first differences).

Programs

Magma

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

Magma

I:=[1, 12, 123]; [n le 3 select I[n] else 13*Self(n-1)-23*Self(n-2)+11*Self(n-3): n in [1..30]];

Mathematica

Table[11^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(- 1 + x + 10 x^2) / ((11 x - 1) (x - 1)^2), {x, 0, 30}], x]
LinearRecurrence[{13,-23,11},{1,12,123},20] (* Harvey P. Dale, Nov 14 2018 *)

PARI

a(n)=11^n+n \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (-1+x+10*x^2)/((11*x-1)*(x-1)^2).

a(n) = 13*a(n-1) - 23*a(n-2) + 11*a(n-3).

E.g.f.: exp(x)*(exp(10*x) + x). - Elmo R. Oliveira, Mar 06 2025