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A171461
a(n) = 1 + 6*10^n + 100^n.
3
8, 161, 10601, 1006001, 100060001, 10000600001, 1000006000001, 100000060000001, 10000000600000001, 1000000006000000001, 100000000060000000001, 10000000000600000000001, 1000000000006000000000001, 100000000000060000000000001, 10000000000000600000000000001, 1000000000000006000000000000001
OFFSET
0,1
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
KEYWORD
nonn,easy
AUTHOR
Jason Earls, Dec 09 2009
EXTENSIONS
More terms from Jinyuan Wang, Feb 25 2020
STATUS
approved