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

Author

Robert Israel, Jun 10 2018

Keywords

• nonn

Comments

For n >= 1, number of terms in A061831 with at most n digits.

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

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).