A064748 a(n) = n*10^n + 1.
1, 11, 201, 3001, 40001, 500001, 6000001, 70000001, 800000001, 9000000001, 100000000001, 1100000000001, 12000000000001, 130000000000001, 1400000000000001, 15000000000000001, 160000000000000001, 1700000000000000001, 18000000000000000001, 190000000000000000001
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Paul Leyland, Cullen and Woodall numbers and their generalization to other bases.
- Index entries for linear recurrences with constant coefficients, signature (21,-120,100).
Programs
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Magma
[ n*10^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011
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Mathematica
Table[n 10^n + 1, {n, 0, 18}] (* Michael De Vlieger, Apr 25 2016 *) -
PARI
a(n) = n*10^n + 1; \\ Altug Alkan, Apr 25 2016
Formula
From Ilya Gutkovskiy, Apr 25 2016: (Start)
O.g.f.: (1 - 10*x + 90*x^2)/((1 - x)*(1 - 10*x)^2).
E.g.f.: (1 + 10*x*exp(9*x))*exp(x). (End)
From Elmo R. Oliveira, May 03 2025: (Start)
a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3).
a(n) = A126431(n) + 1. (End)
Comments