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A363350 Number of n element multisets of length 4 vectors over GF(2) that sum to zero. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, May 30 2023
STATUS
approved

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Last modified July 18 15:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)