A178205 a(n) = a(n-1) + 10*a(n-3) for n > 2; a(0) = a(1) = a(2) = 1.

1, 1, 1, 11, 21, 31, 141, 351, 661, 2071, 5581, 12191, 32901, 88711, 210621, 539631, 1426741, 3532951, 8929261, 23196671, 58526181, 147818791, 379785501, 965047311, 2443235221, 6241090231, 15891563341, 40323915551, 102734817861

Offset: 0

Author

Mark Dols, May 22 2010

Keywords

• nonn
• easy

Comments

If x=a(n), y=a(n+1), z=a(n+2), then 100*x^3 + 10*x^2*z - 30*x*y*z + 10*x*y^2 + 10*y^3 - 2*y*z^2 + y^2*z + z^3 = 10^(n+2), for n >= 0. - Alexander Samokrutov, Jul 03 2015

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,10).

Crossrefs

Cf. A000930 (a(n)=a(n-1)+a(n-3), a(0)=a(1)=a(2)=1).

Programs

Magma

I:=[1,1,1]; [n le 3 select I[n] else Self(n-1) + 10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jul 19 2015

Mathematica

RecurrenceTable[{a[n] == a[n - 1] + 10 a[n - 3], a[0] == a[1] == a[2] == 1}, a, {n, 0, 28}] (* or *)
CoefficientList[Series[1/(1 - x - 10 x^3), {x, 0, 28}], x] (* Michael De Vlieger, Jul 09 2015 *)
LinearRecurrence[{1, 0, 10}, {1, 1, 1}, 30] (* Vincenzo Librandi, Jul 19 2015 *)

PARI

{m=29; v=concat([1, 1, 1], vector(m-3)); for(n=4, m, v[n]=v[n-1]+10*v[n-3]); v}

PARI

x='x+O('x^50); Vec(1/(1-x-10*x^3)) \\ G. C. Greubel, Apr 29 2017

Formula

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

Extensions

Edited and extended by Klaus Brockhaus, May 23 2010