A362906 Number of n element multisets of length 3 vectors over GF(2) that sum to zero.
1, 1, 8, 15, 50, 99, 232, 429, 835, 1430, 2480, 3978, 6372, 9690, 14640, 21318, 30789, 43263, 60280, 82225, 111254, 148005, 195416, 254475, 329095, 420732, 534496, 672452, 841160, 1043460, 1287648, 1577532, 1923465, 2330445, 2811240, 3372291, 4029178
Offset: 0
Examples
The a(1) = 1 multiset is {000}.
The a(2) = 8 multisets are {000, 000}, {001, 001}, {010, 010}, {011, 011}, {100, 100}, {101, 101}, {110, 110}, {111, 111}.
The a(3) = 15 multisets are {000, 000, 000}, {000, 001, 001}, {000, 010, 010}, {000, 011, 011}, {000, 100, 100}, {000, 101, 101}, {000, 110, 110}, {000, 111, 111}, {001, 010, 011}, {001, 100, 101}, {001, 110, 111}, {010, 100, 110}, {010, 101, 111}, {011, 100, 111}, {011, 101, 110}.
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4, -2, -12, 17, 8, -28, 8, 17, -12, -2, 4, -1).
Programs
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Mathematica
A362906[n_]:=(Binomial[n+7,7]+If[EvenQ[n],7Binomial[n/2+3,3],0])/8;Array[A362906,50,0] (* Paolo Xausa, Nov 18 2023 *)
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PARI
a(n) = (binomial(n+7,7) + if(n%2==0, 7*binomial(n/2+3, 3)))/8
Formula
G.f.: (1 - 3*x + 6*x^2 - 3*x^3 + x^4)/((1 - x)^8*(1 + x)^4).
a(n) = binomial(n+7, 7)/8 for odd n;
a(n) = (binomial(n+7, 7) + 7*binomial(n/2+3, 3))/8 for even n.
Comments