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

0,3

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).

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.

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 *)

Prog

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

Crossrefs

Column k=4 of A362905.

Cf. A006382.

Sequence in context: A080860 A204716 A192248 * A297640 A236523 A235660

Adjacent sequences: A363347 A363348 A363349 * A363351 A363352 A363353

Keyword

nonn,easy

Author

Andrew Howroyd, May 30 2023

Status

approved