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A016169 a(n) = 7^n - 6^n. 13
0, 1, 13, 127, 1105, 9031, 70993, 543607, 4085185, 30275911, 222009073, 1614529687, 11664504865, 83828316391, 599858908753, 4277376525367, 30411820662145, 215703854542471, 1526853641242033, 10789535445362647 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)