This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 Vincenzo Librandi, Table of n, a(n) for n = 2..1000 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 * A050885 A200909 A175215 Adjacent sequences:  A210696 A210697 A210698 * A210700 A210701 A210702 KEYWORD nonn,easy AUTHOR R. J. Mathar, Mar 30 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 23 14:36 EDT 2019. Contains 325255 sequences. (Running on oeis4.)