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

%I A363350 #13 Nov 19 2023 08:25:34
%S A363350 1,1,16,51,276,969,3504,10659,30954,81719,205040,482885,1088100,
%T A363350 2340135,4850640,9694845,18789795,35357670,64833120,115997970,
%U A363350 203014680,347993910,585292320,966955410,1571349780,2514084066,3964589856,6167026726,9470900056,14369476066,21554373984
%N A363350 Number of n element multisets of length 4 vectors over GF(2) that sum to zero.
%C A363350 a(n) is the number of n X 4 binary matrices under row permutations and column complementations.
%C A363350 See A362905 for other interpretations.
%H A363350 Andrew Howroyd, <a href="/A363350/b363350.txt">Table of n, a(n) for n = 0..1000</a>
%H A363350 <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A363350 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).
%F A363350 a(n) = binomial(n+15, 15)/16 for odd n;
%F A363350 a(n) = (binomial(n+15, 15) + 15*binomial(n/2+7, 7))/16 for even n.
%t A363350 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 *)
%o A363350 (PARI) a(n) = (binomial(n+15,15) + if(n%2==0, 15*binomial(n/2+7, 7)))/16
%Y A363350 Column k=4 of A362905.
%Y A363350 Cf. A006382.
%K A363350 nonn,easy
%O A363350 0,3
%A A363350 _Andrew Howroyd_, May 30 2023