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
Links
- Index entries for linear recurrences with constant coefficients, signature (17,-70).
Crossrefs
Cf. A248341.
Programs
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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 *) -
PARI
for(n=1,10,print1((10^n-7^n)/3,","))
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)
Extensions
More terms from Elmo R. Oliveira, Mar 26 2025