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A305826 Number of vectors in {0..4}^n with sum divisible by 9. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
For n >= 1, number of terms in A061831 with at most n digits.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9, -36, 114, -216, 270, -222, 117, -36, 5)
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).
EXAMPLE
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].
MAPLE
T:= Matrix(9, shape=Circulant[[1, 0, 0, 0, 0, 1, 1, 1, 1]]):
seq((T^n)[1, 1], n=0..60);
CROSSREFS
Cf. A061831.
Sequence in context: A233176 A156847 A119364 * A252817 A210064 A323223
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 10 2018
STATUS
approved

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Last modified July 24 18:12 EDT 2024. Contains 374585 sequences. (Running on oeis4.)