OFFSET
9,1
COMMENTS
Number of 16-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 9..1000
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
FORMULA
G.f.: 22*(10+3x)*x^9/(1-x)^14.
a(n) = C(n+1, 10)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 02 2022: (Start)
Sum_{n>=9} 1/a(n) = 632045299/12806640 - 5*Pi^2.
Sum_{n>=9} (-1)^(n+1)/a(n) = 5*Pi^2/2 + 96256*log(2)/231 - 4014869821/12806640. (End)
MATHEMATICA
Table[22 (n + 1) Binomial[n + 3, 12], {n, 9, 32}] (* or *) Table[Binomial[n + 1, 10] Binomial[n + 3, 3], {n, 9, 32}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved