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
Links
- Colin Barker, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
Programs
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Mathematica
Join[{8},Table[FromDigits[Join[{1},PadRight[{},n,0],{6},PadRight[{},n,0],{1}]],{n,0,10}]] (* Harvey P. Dale, May 15 2014 *) -
PARI
a(n) = 1 + 6*10^n + 100^n; \\ Jinyuan Wang, Feb 25 2020
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PARI
Vec((8 - 727*x + 1610*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^15)) \\ Colin Barker, Feb 25 2020
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
Extensions
More terms from Jinyuan Wang, Feb 25 2020