OFFSET
0,2
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = A027819(n+1)/7.
a(n) = (n+2)*C(n+7, 7)/2.
G.f.: (1+3*x)/(1-x)^9.
a(n) = C(n+2, 2)*C(n+7, 6)/7. - Zerinvary Lajos, Jul 29 2005
From Amiram Eldar, Feb 11 2022: (Start)
Sum_{n>=0} 1/a(n) = 41783/300 - 14*Pi^2.
Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2 - 2688*log(2)/5 + 91343/300. (End)
MAPLE
a:=n->(sum((numbcomp(n, 8)), j=7..n))/2:seq(a(n), n=8..31); # Zerinvary Lajos, Aug 26 2008
MATHEMATICA
Table[(n + 2)*Binomial[n + 7, 7]/2, {n, 0, 40}] (* Amiram Eldar, Feb 11 2022 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 12, 72, 300, 990, 2772, 6864, 15444, 32175}, 40] (* Harvey P. Dale, Sep 06 2024 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jan 26 2000
STATUS
approved