A016169 a(n) = 7^n - 6^n.

0, 1, 13, 127, 1105, 9031, 70993, 543607, 4085185, 30275911, 222009073, 1614529687, 11664504865, 83828316391, 599858908753, 4277376525367, 30411820662145, 215703854542471, 1526853641242033, 10789535445362647

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is also the number of n-digit numbers whose smallest decimal digit is 3. - Stefano Spezia, Nov 15 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• John Elias, Illustration of initial terms: a star number fractal
• Index entries for linear recurrences with constant coefficients, signature (13,-42).

Crossrefs

Cf. A005062, A016177, A016189, A081201.

Programs

Magma

[n le 2 select n-1 else 13*Self(n-1) -42*Self(n-2): n in [1..31]]; // G. C. Greubel, Nov 10 2024

Maple

a:=n->sum(6^(n-j)*binomial(n,j),j=1..n): seq(a(n), n=0..30); # Zerinvary Lajos, Apr 18 2009

Mathematica

Table[7^n-6^n,{n,0,30}] (* or *) LinearRecurrence[{13,-42},{0,1},30] (* Harvey P. Dale, Apr 25 2020 *)

SageMath

A016169=BinaryRecurrenceSequence(13,-42,0,1)
[A016169(n) for n in range(41)] # G. C. Greubel, Nov 10 2024

Formula

G.f.: x/((1-6*x)*(1-7*x)).

E.g.f.: exp(7*x) - exp(6*x). - Mohammad K. Azarian, Jan 14 2009

a(0)=0, a(n) = 7*a(n-1) + 6^(n-1). - Vincenzo Librandi, Feb 09 2011

a(0)=0, a(1)=1, a(n) = 13*a(n-1) - 42*a(n-2). - Vincenzo Librandi, Feb 09 2011