A363350 Number of n element multisets of length 4 vectors over GF(2) that sum to zero.

1, 1, 16, 51, 276, 969, 3504, 10659, 30954, 81719, 205040, 482885, 1088100, 2340135, 4850640, 9694845, 18789795, 35357670, 64833120, 115997970, 203014680, 347993910, 585292320, 966955410, 1571349780, 2514084066, 3964589856, 6167026726, 9470900056, 14369476066, 21554373984

Offset: 0

Author

Andrew Howroyd, May 30 2023

Keywords

• nonn
• easy

Comments

a(n) is the number of n X 4 binary matrices under row permutations and column complementations.

See A362905 for other interpretations.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8, -20, -8, 126, -168, -196, 680, -239, -1072, 1240, 560, -1820, 560, 1240, -1072, -239, 680, -196, -168, 126, -8, -20, 8, -1).

Crossrefs

Column k=4 of A362905.

Cf. A006382.

Programs

Mathematica

A363350[n_]:=(Binomial[n+15,15]+If[EvenQ[n],15Binomial[n/2+7,7],0])/16;Array[A363350,50,0] (* Paolo Xausa, Nov 18 2023 *)

PARI

a(n) = (binomial(n+15,15) + if(n%2==0, 15*binomial(n/2+7, 7)))/16

Formula

G.f.: (1 - 7*x + 28*x^2 - 49*x^3 + 70*x^4 - 49*x^5 + 28*x^6 - 7*x^7 + x^8)/((1 - x)^16*(1 + x)^8).

a(n) = binomial(n+15, 15)/16 for odd n;

a(n) = (binomial(n+15, 15) + 15*binomial(n/2+7, 7))/16 for even n.