OFFSET
1,2
COMMENTS
a(k(n)) is divisible by 3 iff k(n) is defined by k(1) = 5 and k(n+1) - k(n) = A100285(n+2). - Altug Alkan, Dec 05 2015
LINKS
Matthew Schulz, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (11,-20,110,-100).
FORMULA
From R. J. Mathar, Feb 20 2009: (Start)
a(n) = 11*a(n-1)-20*a(n-2)+110*a(n-3)-100*a(n-4).
G.f.: x/((1-x)*(1-10*x)*(1+10*x^2)). (End)
E.g.f.: (exp(x)*(10*exp(9*x) - 1) - 9*cos(sqrt(10)*x))/99. - Stefano Spezia, Oct 12 2024
EXAMPLE
n .... Successive digits of a(n)
1 ............. ( 1 )
2 ............ ( 1 1 )
3 ........... ( 1 0 1 )
4 .......... ( 1 0 0 1 )
5 ......... ( 1 0 1 0 1 )
6 ........ ( 1 0 1 1 0 1 )
7 ....... ( 1 0 1 0 1 0 1 )
8 ...... ( 1 0 1 0 0 1 0 1 )
9 ..... ( 1 0 1 0 1 0 1 0 1 )
10 ... ( 1 0 1 0 1 1 0 1 0 1 )
MATHEMATICA
CoefficientList[Series[x/((1 - x) (1 - 10 x) (1 + 10 x^2)), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 05 2015 *)
LinearRecurrence[{11, -20, 110, -100}, {1, 11, 101, 1001}, 30] (* Harvey P. Dale, Apr 10 2022 *)
PROG
(PARI) Vec(x/((1-x)*(1-10*x)*(1+10*x^2)) + O(x^30)) \\ Michel Marcus, Dec 05 2015
(Magma) I:=[1, 11, 101, 1001]; [n le 4 select I[n] else 11*Self(n-1)-20*Self(n-2)+110*Self(n-3)-100*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 05 2015
CROSSREFS
KEYWORD
base,easy,nonn,changed
AUTHOR
Omar E. Pol, Nov 11 2008
STATUS
approved