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 A027790 a(n) = 10*(n+1)*binomial(n+3,5)/3. 1

%I

%S 10,80,350,1120,2940,6720,13860,26400,47190,80080,130130,203840,

%T 309400,456960,658920,930240,1288770,1755600,2355430,3116960,4073300,

%U 5262400,6727500,8517600,10687950,13300560,16424730,20137600

%N a(n) = 10*(n+1)*binomial(n+3,5)/3.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).

%F Number of 9-subsequences of [ 1, n ] with just 3 contiguous pairs.

%F G.f.: 10*(1+x)*x^2/(1-x)^7.

%F a(n) = binomial(n+1, 3)*binomial(n+3, 3) = A000292(n-1)*A000292(n+1). - _Zerinvary Lajos_, May 13 2005

%F a(n) = 10*A040977(n). - _R. J. Mathar_, May 22 2013

%t Table[10(n+1) Binomial[n+3,5]/3,{n,2,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{10,80,350,1120,2940,6720,13860},30] (* _Harvey P. Dale_, Jan 15 2015 *)

%K nonn,easy

%O 2,1

%A thi ngoc dinh (via _R. K. Guy_)

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)