A305826 Number of vectors in {0..4}^n with sum divisible by 9.
1, 1, 1, 11, 81, 381, 1673, 8338, 43585, 220037, 1086581, 5401793, 27090649, 135792879, 678626796, 3389980516, 16949548097, 84773530931, 423896384077, 2119296824851, 10596060837121, 52981415499506, 264911698225527, 1324553898108366, 6622726587716561, 33113628115834381, 165568491457714333
Offset: 0
Keywords
Examples
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].
Links
- Robert Israel, Table of n, a(n) for n = 0..1430
- Index entries for linear recurrences with constant coefficients, signature (9, -36, 114, -216, 270, -222, 117, -36, 5)
Crossrefs
Cf. A061831.
Programs
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Maple
T:= Matrix(9,shape=Circulant[[1,0,0,0,0,1,1,1,1]]): seq((T^n)[1,1],n=0..60);
Formula
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).
Comments