A024050 a(n) = 5^n - n.

1, 4, 23, 122, 621, 3120, 15619, 78118, 390617, 1953116, 9765615, 48828114, 244140613, 1220703112, 6103515611, 30517578110, 152587890609, 762939453108, 3814697265607, 19073486328106, 95367431640605, 476837158203104, 2384185791015603, 11920928955078102, 59604644775390601

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Crossrefs

Cf. numbers of the form k^n - n: A000325 (k=2), A024024 (k=3), A024037 (k=4), this sequence (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).

Programs

Magma

[5^n-n: n in [0..35]]; // Vincenzo Librandi, Jun 12 2011

Maple

g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-n, n=0..31); # Zerinvary Lajos, Jan 09 2009

Mathematica

Table[5^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 6 x^2) / ((1 - 5 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)
LinearRecurrence[{7,-11,5},{1,4,23},30] (* Harvey P. Dale, Mar 03 2022 *)

Formula

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).

G.f.: (1 - 3*x + 6*x^2)/((1-5*x)*(1-x)^2). - Vincenzo Librandi, Jun 16 2013

E.g.f.: exp(x)*(exp(4*x) - x). - Elmo R. Oliveira, Sep 10 2024