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A374542
Number of length n inversion sequences avoiding the patterns 102 and 210.
4
1, 1, 2, 6, 22, 87, 351, 1416, 5681, 22660, 89961, 355924, 1404839, 5536143, 21794634, 85749490, 337271186, 1326421512, 5216761708, 20520185594, 80733298320, 317713643536, 1250674963766, 4924782835110, 19398524629494, 76434881013402, 301270165265954
OFFSET
0,3
FORMULA
G.f: ((4*x - 1) * (4*x^4 - 22*x^3 + 25*x^2 - 9*x + 1) - (2*x - 1) * (x^2 - 5*x + 1) * (2*x^2 - 4*x + 1) * (1-4*x)^(1/2)) / (2*x^3 * (4*x - 1) * (x - 1)^2).
D-finite with recurrence -(n+3)*(1514*n-13441)*a(n) +(16281*n^2-104929*n-159699)*a(n-1) +(-54702*n^2+377288*n-136533)*a(n-2) +(60299*n^2-430394*n+520290)*a(n-3) -6*(2*n-7)*(1697*n-7015)*a(n-4) +30*(-702*n+3361)=0. - R. J. Mathar, Jul 12 2024
CROSSREFS
Cf. A279555.
Sequence in context: A153475 A150259 A165531 * A150260 A165532 A165533
KEYWORD
nonn
AUTHOR
Benjamin Testart, Jul 12 2024
STATUS
approved