A322927 Expansion of x*(1 + 5*x + 40*x^2)/((1 - x^2)*(1 - 10*x^2)).

0, 1, 5, 51, 55, 551, 555, 5551, 5555, 55551, 55555, 555551, 555555, 5555551, 5555555, 55555551, 55555555, 555555551, 555555555, 5555555551, 5555555555, 55555555551, 55555555555, 555555555551, 555555555555, 5555555555551, 5555555555555, 55555555555551

Offset: 0

Author

Vincenzo Librandi, Mar 17 2019

Keywords

• nonn
• easy

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).

Crossrefs

Bisections give: A002279 (even part), A173804 (odd part).

Programs

Magma

I:=[0, 1, 5, 51]; [n le 4 select I[n] else 11*Self(n-2)-10*Self(n-4): n in [1..30]];

Maple

seq(coeff(series(x*(1+5*x+40*x^2)/((1-x^2)*(1-10*x^2)),x,n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Mar 17 2019

Mathematica

CoefficientList[Series[x (1 + 5 x + 40 x^2) / (10 x^4 - 11 x^2 + 1), {x, 0, 25}], x]

Formula

G.f.: x*(1 + 5*x + 40*x^2)/((1 - x^2)*(1 - 10*x^2)).

a(n) = 11*a(n-2) - 10*a(n-4).

a(n) = 5*(10^n - 1)/9 for n even; a(n) = (5*10^n - 41)/9 otherwise.