A248341 a(n) = 10^n - 7^n.

0, 3, 51, 657, 7599, 83193, 882351, 9176457, 94235199, 959646393, 9717524751, 98022673257, 986158712799, 9903110989593, 99321776927151, 995252438490057, 9966767069430399, 99767369486012793, 998371586402089551, 9988601104814626857

Offset: 0

Author

Vincenzo Librandi, Oct 05 2014

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (17,-70).

Crossrefs

Cf. sequences of the form k^n-7^n: A016177 (k=8), A191467 (k=9), this sequence(k=10), A139745 (k=11).

Cf. A000420, A011557, A016181.

Programs

Magma

[10^n-7^n: n in [0..30]];

Mathematica

Table[10^n - 7^n, {n, 0, 25}] (* or *) CoefficientList[Series[3 x/((1 - 7 x) (1 - 10 x)), {x, 0, 30}], x]
LinearRecurrence[{17,-70},{0,3},20] (* Harvey P. Dale, Dec 18 2020 *)

Formula

G.f.: 3*x/((1-7*x)*(1-10*x)).

a(n) = 17*a(n-1) - 70*a(n-2).

a(n) = A011557(n) - A000420(n).

a(n+1) = 3*A016181(n).

E.g.f.: 2*exp(17*x/2)*sinh(3*x/2). - Elmo R. Oliveira, Apr 01 2025