A171461 a(n) = 1 + 6*10^n + 100^n.

8, 161, 10601, 1006001, 100060001, 10000600001, 1000006000001, 100000060000001, 10000000600000001, 1000000006000000001, 100000000060000000001, 10000000000600000000001, 1000000000006000000000001, 100000000000060000000000001, 10000000000000600000000000001, 1000000000000006000000000000001

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

From Colin Barker, Feb 25 2020: (Start)

G.f.: (8 - 727*x + 1610*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.

(End)

E.g.f.: exp(x)*(1 + 6*exp(9*x) + exp(99*x)). - Stefano Spezia, Feb 25 2020

Mathematica

Join[{8}, Table[FromDigits[Join[{1}, PadRight[{}, n, 0], {6}, PadRight[{}, n, 0], {1}]], {n, 0, 10}]] (* Harvey P. Dale, May 15 2014 *)

Prog

(PARI) a(n) = 1 + 6*10^n + 100^n; \\ Jinyuan Wang, Feb 25 2020
(PARI) Vec((8 - 727*x + 1610*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^15)) \\ Colin Barker, Feb 25 2020

Crossrefs

Sequence in context: A245322 A305524 A326099 * A065116 A240410 A061250

Adjacent sequences: A171458 A171459 A171460 * A171462 A171463 A171464

Keyword

nonn,easy

Author

Jason Earls, Dec 09 2009

Extensions

More terms from Jinyuan Wang, Feb 25 2020

Status

approved