A179619 a(1)=1, a(n+1) = 10*a(n)+2*n-1

1, 13, 135, 1357, 13579, 135801, 1358023, 13580245, 135802467, 1358024689, 13580246911, 135802469133, 1358024691355, 13580246913577, 135802469135799, 1358024691358021, 13580246913580243, 135802469135802465, 1358024691358024687, 13580246913580246909

Offset

1,2

Comments

Third column of A164851. The repeating pattern corresponds to the decimal expansion of 11/81 = 0.13580246913580246...

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Formula

a(1)=1, a(2)=13, a(3)=135, a(n) = 12*a(n-1)-21*a(n-2)+10*a(n-3). - Harvey P. Dale, Aug 16 2012

G.f.: -x*(x+1) / ((x-1)^2*(10*x-1)). - Colin Barker, Oct 03 2015

Mathematica

RecurrenceTable[{a[1] == 1, a[n] == 10 a[n - 1] + 2 n - 1}, a, {n,
30}] (* or *) LinearRecurrence[{12, -21, 10}, {1, 13, 135}, 30] (* Harvey P. Dale, Aug 16 2012 *)

Prog

(PARI) Vec(-x*(x+1)/((x-1)^2*(10*x-1)) + O(x^30)) \\ Colin Barker, Oct 03 2015

Crossrefs

Cf. A164851.

Sequence in context: A132935 A132930 A130774 * A019519 A243216 A112225

Adjacent sequences: A179616 A179617 A179618 * A179620 A179621 A179622

Keyword

nonn,easy

Author

Mark Dols, Jul 20 2010

Status

approved