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A193108 The tetrahedral numbers A000292 mod 10.

%I A193108 #30 Aug 27 2015 10:30:53
%S A193108 1,4,0,0,5,6,4,0,5,0,6,4,5,0,0,6,9,0,0,0,1,4,0,0,5,6,4,0,5,0,6,4,5,0,
%T A193108 0,6,9,0,0,0,1,4,0,0,5,6,4,0,5,0,6,4,5,0,0,6,9,0,0,0,1,4,0,0,5,6,4,0,
%U A193108 5,0,6,4,5,0,0,6,9,0,0,0,1,4,0,0,5,6,4,0,5,0,6,4,5,0,0,6,9,0,0,0
%N A193108 The tetrahedral numbers A000292 mod 10.
%C A193108 Periodic with period 20.
%C A193108 The cycle is symmetric about index 9 in that a(8)+a(10), a(7)+a(11), etc are all congruent to 0 mod 10.
%C A193108 If the first diagonal of Pascal's triangle is given index 0 this sequence is the 3rd diagonal of Pascal's triangle modulo 10, or the binomial coefficients C(n+2,3)mod 10. Note that the last three terms in the cycle are 0.
%C A193108 The Pisano period lengths of A000292 (mod m) are 1,  4,  9,  8,  5, 36,  7, 16, 27, 20, 11, 72, 13, 28, 45, 32, 17,108, 19, 40.., for m>=1. This sequence describes the case m=10. - R. J. Mathar, Oct 25 2011
%H A193108 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A193108 a(n) = a(n-20).
%F A193108 G.f.  -x*(1+4*x+5*x^4+6*x^5+4*x^6+5*x^8+6*x^10+4*x^11+5*x^12+6*x^15+9*x^16)  / ( (x-1)*(1+x^4+x^3+x^2+x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x^2)*(x^8-x^6+x^4-x^2+1) ). - _R. J. Mathar_, Oct 25 2011
%F A193108 a(n) = 55 -a(n-1) -a(n-2) … -a(n-18) -a(n-19). - _Ant King_, Oct 19 2012
%t A193108 Table[Mod[Binomial[n+2,3],10],{n,1,21}]
%Y A193108 Cf. A000292, A008954.
%K A193108 nonn,easy
%O A193108 1,2
%A A193108 _Chris Fry_, Jul 16 2011
%E A193108 Edited by _N. J. A. Sloane_, Jul 16 2011