OFFSET
1,2
COMMENTS
This is a periodic sequence with period 20 and cycle 1, 9, 4, 6, 5, 1, 4, 4, 1, 5, 6, 4, 9, 1, 0, 6, 9, 9, 6, 0.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,0,0,-1,0,0,0,0,1).
FORMULA
a(n) = a(n-20).
a(n) = a(n-5) - a(n-10) + a(n-15).
a(n) = 45 - a(n-1) - a(n-2) - a(n-3) - a(n-4) - a(n-10) - a(n-11) - a(n-12) - a(n-13) - a(n-14).
a(n) = 90 - a(n-1) - a(n-2) - a(n-3) - ... - a(n-17) - a(n-18) - a(n-19).
a(n) = (1/2 n(7n-5)) mod 10.
G.f.: x*(1+9*x+4*x^2+6*x^3+5*x^4-5*x^6-5*x^8+6*x^10+9*x^11+9*x^12+6*x^13)/((1-x)*(1+x^2)*(1+x+x^2+x^3+x^4)*(1-x^2+x^4-x^6+x^8)). - Bruno Berselli, Sep 05 2011
EXAMPLE
The seventh nonzero 9-gonal (nonagonal) number is A001106(7)=154, which has units' digit 4. Hence a(7)=4.
MATHEMATICA
Table[Mod[n*(7*n-5)/2, 10], {n, 86}]
PROG
(Magma) [(Floor(n*(7*n-5)/2)) mod (10): n in [1..80]]; // Vincenzo Librandi, Sep 06 2011
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Ant King, Sep 04 2011
STATUS
approved