A016181 Expansion of g.f. 1/((1-7*x)*(1-10*x)).

1, 17, 219, 2533, 27731, 294117, 3058819, 31411733, 319882131, 3239174917, 32674224419, 328719570933, 3301036996531, 33107258975717, 331750812830019, 3322255689810133, 33255789828670931, 332790528800696517, 3329533701604875619, 33306735911234129333, 333147151378638905331

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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

Formula

a(n) = (10^(n+1) - 7^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005

From Vincenzo Librandi, Feb 09 2011: (Start)

a(n) = 10*a(n-1) + 7^n, a(0)=1.

a(n) = 17*a(n-1) - 70*a(n-2), a(0)=1, a(1)=17. (End)

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(7*x)*(10*exp(3*x) - 7)/3.

a(n) = A248341(n+1)/3. (End)

Mathematica

Join[{a=1, b=17}, Table[c=17*b-70*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
CoefficientList[Series[1/((1-7x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {17, -70}, {1, 17}, 30] (* Harvey P. Dale, Nov 16 2020 *)

Prog

(PARI) for(n=1, 10, print1((10^n-7^n)/3, ", "))

Crossrefs

Cf. A248341.

Sequence in context: A125452 A322538 A016238 * A285233 A063043 A016174

Adjacent sequences: A016178 A016179 A016180 * A016182 A016183 A016184

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Elmo R. Oliveira, Mar 26 2025

Status

approved