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A305826 Number of vectors in {0..4}^n with sum divisible by 9.

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%I A305826 #12 Jun 11 2018 03:07:34
%S A305826 1,1,1,11,81,381,1673,8338,43585,220037,1086581,5401793,27090649,
%T A305826 135792879,678626796,3389980516,16949548097,84773530931,423896384077,
%U A305826 2119296824851,10596060837121,52981415499506,264911698225527,1324553898108366,6622726587716561,33113628115834381,165568491457714333
%N A305826 Number of vectors in {0..4}^n with sum divisible by 9.
%C A305826 For n >= 1, number of terms in A061831 with at most n digits.
%H A305826 Robert Israel, <a href="/A305826/b305826.txt">Table of n, a(n) for n = 0..1430</a>
%H A305826 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 114, -216, 270, -222, 117, -36, 5)
%F A305826 G.f.: (1-8*x+28*x^2-76*x^3+120*x^4-120*x^5+74*x^6-26*x^7+4*x^8) / (1 - 9*x + 36*x^2 - 114*x^3 + 216*x^4 - 270*x^5 + 222*x^6 - 117*x^7 + 36*x^8 - 5*x^9).
%e A305826 For n=3, the a(3)=11 vectors are [0, 0, 0], [1, 4, 4], [2, 3, 4], [2, 4, 3], [3, 2, 4], [3, 3, 3], [3, 4, 2], [4, 1, 4], [4, 2, 3], [4, 3, 2], [4, 4, 1].
%p A305826 T:= Matrix(9,shape=Circulant[[1,0,0,0,0,1,1,1,1]]):
%p A305826 seq((T^n)[1,1],n=0..60);
%Y A305826 Cf. A061831.
%K A305826 nonn
%O A305826 0,4
%A A305826 _Robert Israel_, Jun 10 2018