A027803 a(n) = 35*(n+1)*binomial(n+4, 7)/4.

35, 350, 1890, 7350, 23100, 62370, 150150, 330330, 675675, 1301300, 2382380, 4176900, 7054320, 11531100, 18314100, 28352940, 42902475, 63596610, 92534750, 132382250, 186486300, 259008750, 355077450, 480957750, 644245875

Offset

3,1

Comments

Number of 12-subsequences of [ 1, n ] with just 4 contiguous pairs.

Links

Table of n, a(n) for n=3..27.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = 35*A053347(n-3).

G.f.: 35*(1+x)*x^3/(1-x)^9.

a(n) = C(n+1, 4)*C(n+4, 4). - Zerinvary Lajos, May 10 2005, corrected by R. J. Mathar, Mar 16 2016

From Amiram Eldar, Jan 25 2022: (Start)

Sum_{n>=3} 1/a(n) = 5929/225 - 8*Pi^2/3.

Sum_{n>=3} (-1)^(n+1)/a(n) = 4*Pi^2/3 - 197/15. (End)

Mathematica

Table[35 (n + 1) Binomial[n + 4, 7]/4, {n, 3, 30}] (* or *) Table[Binomial[n + 1, 4] Binomial[n + 4, 4], {n, 3, 30}] (* Michael De Vlieger, Mar 16 2016 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {35, 350, 1890, 7350, 23100, 62370, 150150, 330330, 675675}, 30] (* Harvey P. Dale, May 07 2022 *)

Crossrefs

Cf. A053347, A062145.

Sequence in context: A027792 A163935 A101099 * A267749 A073567 A225697

Adjacent sequences: A027800 A027801 A027802 * A027804 A027805 A027806

Keyword

nonn,easy

Author

Thi Ngoc Dinh (via R. K. Guy)

Status

approved