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
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 30 2012
STATUS
approved