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

Author

Mark Dols, Jul 20 2010

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A164851.

Programs

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 *)

PARI

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

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