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A027793 a(n) = 28*(n+1)*binomial(n+3,8)/3. 0
56, 588, 3360, 13860, 46200, 132132, 336336, 780780, 1681680, 3403400, 6534528, 11992344, 21162960, 36085560, 59690400, 96101544, 151016712, 232178100, 349949600, 518017500, 754233480, 1081620540, 1529564400, 2135214900, 2945124000, 4017149136, 5422652928 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,1
COMMENTS
Number of 12-subsequences of [ 1, n ] with just 3 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.: 28*(2+x)*x^5/(1-x)^10.
a(n) = C(n+1, 6)*C(n+3, 3). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=5} 1/a(n) = 145181/4900 - 3*Pi^2.
Sum_{n>=5} (-1)^(n+1)/a(n) = 3*Pi^2/2 + 2112*log(2)/35 - 277411/4900. (End)
MATHEMATICA
Table[28(n+1) Binomial[n+3, 8]/3, {n, 5, 30}] (* Harvey P. Dale, Oct 24 2020 *)
CROSSREFS
Sequence in context: A219712 A244429 A005931 * A244945 A055747 A234106
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved

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Last modified March 2 06:08 EST 2024. Contains 370460 sequences. (Running on oeis4.)