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A210699
Number of bilaterally asymmetric 8-hoops with n symbols and no a-rooted trees.
3
1, 71, 918, 6667, 33665, 131616, 425866, 1192178, 2977857, 6785605, 14339006, 28451061, 53519713, 96176822, 166119570, 277155796, 448497281, 706337523, 1085753062, 1632969935, 2408039361, 3487969276, 4970360858, 6977601702, 9661669825, 13209605201, 17849708046
OFFSET
2,2
COMMENTS
Follows from the polynomial of eq (29) in the Williamson paper and differs from A210768 (the published version) in a(3) and a(5).
LINKS
Williamson, S. G. The combinatorial analysis of patterns and the principle of inclusion-exclusion. Discrete Math. 1 (1972), no. 4, 357--388. MR0299493 (45 #8541)
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = (n-1)*(n^7-7*n^6+29*n^5-71*n^4+116*n^3-128*n^2+80*n-32)/16.
G.f.: x^2*(1+62*x+315*x^2+877*x^3+872*x^4+351*x^5+40*x^6+2*x^7)/(1-x)^9. [Colin Barker, Apr 01 2012]
a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). Vincenzo Librandi, May 13 2012
MAPLE
A210768 := proc(n)
(n^8 -8*n^7 +36*n^6 -100*n^5 +187*n^4 -244*n^3 +208*n^2 -112*n+32)/16 ;
end proc:
seq(A210768(n), n=2..20) ;
MATHEMATICA
CoefficientList[Series[(1+62*x+315*x^2+877*x^3+872*x^4+351*x^5+ 40*x^6+ 2*x^7)/(1-x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2012 *)
PROG
(Magma) I:=[1, 71, 918, 6667, 33665, 131616, 425866, 1192178, 2977857]; [n le 9 select I[n] else 9*Self(n-1)-36*Self(n-2)+84*Self(n-3)-126*Self(n-4)+126*Self(n-5)-84*Self(n-6)+36*Self(n-7)-9*Self(n-8)+Self(n-9): n in [1..30]]; // Vincenzo Librandi, May 13 2012
CROSSREFS
Sequence in context: A220623 A173806 A253683 * A346023 A050885 A200909
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 30 2012
STATUS
approved