A321311 Number of linear chord diagrams having n+2 chords and minimal chord length n.
10, 26, 79, 252, 796, 2468, 7564, 23012, 69676, 210308, 633484, 1905572, 5726956, 17201348, 51645004, 155016932, 465214636, 1395971588, 4188570124, 12567021092, 37703684716, 113116297028, 339359376844, 1018099102052, 3054339249196, 9163101633668, 27489472673164
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (5, -6)
Programs
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Mathematica
Join[{10, 26, 79}, LinearRecurrence[{5, -6}, {252, 796}, 24]] (* Jean-François Alcover, Nov 24 2018 *) -
PARI
Vec((10 - 24*x + 9*x^2 + 13*x^3 + 10*x^4)/((1 - 2*x)*(1 - 3*x)) + O(x^40)) \\ Andrew Howroyd, Nov 17 2018
Formula
a(n) = A293881(n+2,n).
a(n) = 5*a(n-1) - 6*a(n-2) for n > 5.
a(n) = A293156(n) - 5*2^(n-1).
G.f.: x*(10 - 24*x + 9*x^2 + 13*x^3 + 10*x^4)/((1 - 2*x)*(1 - 3*x)). - Andrew Howroyd, Nov 17 2018
2*3^4*a(n) = 2^3*73*3^n-5*3^4*2^n for n>3. - R. J. Mathar, Jan 25 2023