A322925 Expansion of x*(1 + 2*x + 10*x^2)/((1 - x^2)*(1 - 10*x^2)).

0, 1, 2, 21, 22, 221, 222, 2221, 2222, 22221, 22222, 222221, 222222, 2222221, 2222222, 22222221, 22222222, 222222221, 222222222, 2222222221, 2222222222, 22222222221, 22222222222, 222222222221, 222222222222, 2222222222221, 2222222222222, 22222222222221

Offset

0,3

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).

Formula

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

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

a(n) = 2*(10^n - 1)/9 for n even; a(n) = (2*10^n - 11)/9 otherwise.

a(n) = (2/9)*10^floor((n + 1)/2) + (-1)^n/2 - 13/18. - Bruno Berselli, Mar 16 2019

Maple

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

Mathematica

CoefficientList[Series[x (1 + 2 x + 10 x^2)/((1 - x^2) (1 - 10 x^2)), {x, 0, 33}], x]
LinearRecurrence[{0, 11, 0, -10}, {0, 1, 2, 21}, 30] (* Harvey P. Dale, Mar 02 2021 *)

Prog

(Magma) I:=[0, 1, 2, 21]; [n le 4 select I[n] else 11*Self(n-2)-10*Self(n-4): n in [1..30]]
(GAP) a:=[0, 1, 2, 21];; for n in [5..30] do a[n]:=11*a[n-2]-10*a[n-4]; od; Print(a); # Muniru A Asiru, Apr 10 2019

Crossrefs

Bisections give: A002276 (even part), A165402 (odd part).

Sequence in context: A359385 A110301 A233135 * A294116 A041513 A135053

Adjacent sequences: A322922 A322923 A322924 * A322926 A322927 A322928

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2019

Status

approved