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

0,3

Comments

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

Links

Table of n, a(n) for n=0..19.

John Elias, Illustration of initial terms: a star number fractal

Index entries for linear recurrences with constant coefficients, signature (13,-42).

Formula

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

E.g.f.: e^(7*x) - e^(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]

Maple

a:=n->sum(6^(n-j)*binomial(n, j), j=1..n): seq(a(n), n=0..19); # Zerinvary Lajos, Apr 18 2009

Mathematica

Table[7^n-6^n, {n, 0, 20}] (* or *) LinearRecurrence[{13, -42}, {0, 1}, 20] (* Harvey P. Dale, Apr 25 2020 *)

Crossrefs

Cf. A016177, A016189.

Sequence in context: A202122 A201086 A139786 * A125401 A089763 A124298

Adjacent sequences: A016166 A016167 A016168 * A016170 A016171 A016172

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved