OFFSET
1,2
COMMENTS
The members of this sequence are also the units' digits of the indices of those nonzero square numbers that are also triangular.
The coefficients of x^n in the numerator of the generating function form the periodic cycle of the sequence.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
FORMULA
G.f.: x*(1+6*x+5*x^2+4*x^3+9*x^4) / ((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)).
a(n) = a(n-6) for n>6.
a(n) = 25 - a(n-1) - a(n-2) - a(n-3) - a(n-4) - a(n-5) for n>5.
a(n) = (25-5*cos(n*Pi)-10*cos(n*Pi/3)-10*cos(2*n*Pi/3)-2*sqrt(3)*(3*sin(n*Pi/3)+5*sin(2*n*Pi/3)))/6. - Wesley Ivan Hurt, Jun 18 2016
EXAMPLE
The fourth nonzero square number that is also a triangular number is 204^2. As 204 has units' digit 4, then a(4)=4.
MAPLE
A205651:=n->(25-5*cos(n*Pi)-10*cos(n*Pi/3)-10*cos(2*n*Pi/3)-2*sqrt(3)*(3*sin(n*Pi/3)+5*sin(2*n*Pi/3)))/6: seq(A205651(n), n=1..100); # Wesley Ivan Hurt, Jun 18 2016
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 6, 5, 4, 9, 0}, 86]
PadRight[{}, 120, {1, 6, 5, 4, 9, 0}] (* Vincenzo Librandi, Jun 19 2016 *)
PROG
(PARI) a(n)=[0, 1, 6, 5, 4, 9][n%6+1] \\ Charles R Greathouse IV, Jan 31 2012
(Magma) &cat[[1, 6, 5, 4, 9, 0]: n in [0..20]]; // Wesley Ivan Hurt, Jun 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ant King, Jan 31 2012
STATUS
approved