OFFSET
4,1
COMMENTS
Number of 13-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: 14*(5+4x)*x^4/(1-x)^10.
a(n) = C(n+1, 5)*C(n+4, 4). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=4} 1/a(n) = 10*Pi^2/3 - 145013/4410.
Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/3 + 128*log(2)/7 - 42793/1470. (End)
MATHEMATICA
Table[14 * (n+1) * Binomial[n+4, 8], {n, 4, 50}] (* Amiram Eldar, Feb 04 2022 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {70, 756, 4410, 18480, 62370, 180180, 462462, 1081080, 2342340, 4764760}, 30] (* Harvey P. Dale, Aug 26 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved