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A293997
Number of linear chord diagrams having n chords and no chord length larger than five.
2
1, 1, 3, 15, 105, 945, 3465, 14857, 72905, 393565, 2152693, 10317169, 49808117, 247455873, 1256019673, 6371895677, 31696702545, 157383838325, 785587613797, 3938599251649, 19742522444733, 98655068282297, 492637126850897, 2462204077446773, 12316715419452585
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, 4, 2, 81, 495, -648, -1590, 208, -5670, -924, 14576, -1536, -2136, -9936, 10656, -2880)
FORMULA
G.f.: -(24*x^11-84*x^10+76*x^9+20*x^8-10*x^7-90*x^6+12*x^5+35*x^4+4*x^2+2*x-1) / ((5*x-1) *(576*x^15 -2016*x^14 +1584*x^13 +744*x^12 +456*x^11 -2824*x^10 -380*x^9 +1058*x^8 +170*x^7 +352*x^6 +200*x^5 -59*x^4 -28*x^3 -6*x^2 -2*x-1)).
MATHEMATICA
CoefficientList[Series[-(24x^11-84x^10+76x^9+20x^8-10x^7-90x^6+12x^5+35x^4+4x^2+2x-1)/((5x-1)(576x^15-2016x^14+1584x^13+744x^12+ 456x^11- 2824x^10-380x^9+ 1058x^8+ 170x^7+352x^6+200x^5-59x^4-28x^3-6x^2-2x-1)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {3, 4, 2, 81, 495, -648, -1590, 208, -5670, -924, 14576, -1536, -2136, -9936, 10656, -2880}, {1, 1, 3, 15, 105, 945, 3465, 14857, 72905, 393565, 2152693, 10317169, 49808117, 247455873, 1256019673, 6371895677}, 30] (* Harvey P. Dale, Jan 03 2024 *)
CROSSREFS
Column k=5 of A293960.
Sequence in context: A251598 A338725 A295871 * A328866 A247304 A293998
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 21 2017
STATUS
approved