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A105450 a(n) = binomial(n+5,6) + binomial(n+3,3) + binomial(n+2,3) + binomial(n-1,1).

%I A105450 #16 Nov 14 2016 14:17:03
%S A105450 0,6,22,60,142,305,607,1134,2008,3396,5520,8668,13206,19591,28385,
%T A105450 40270,56064,76738,103434,137484,180430,234045,300355,381662,480568,
%U A105450 600000,743236,913932,1116150,1354387,1633605,1959262,2337344,2774398,3277566,3854620
%N A105450 a(n) = binomial(n+5,6) + binomial(n+3,3) + binomial(n+2,3) + binomial(n-1,1).
%C A105450 Number of directed column-convex polyominoes with perimeter 2(n+4) having n cells in the foundational column.
%C A105450 A051743 and this sequence form successive diagonals in an array that has as row sums the sequence A006027.
%H A105450 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A105450 a(0)=0, a(1)=6, a(2)=22, a(3)=60, a(4)=142, a(5)=305, a(6)= 607, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+a(n-7). - _Harvey P. Dale_, Jun 28 2011
%F A105450 G.f.: (2*x^6-11*x^5+26*x^4-32*x^3+20*x^2-6*x)/(x-1)^7. - _Harvey P. Dale_, Jun 28 2011
%t A105450 Table[Binomial[n+5,6]+Binomial[n+3,3]+Binomial[n+2,3]+ Binomial[n-1,1],{n,0,50}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,6,22,60,142,305,607},51] (* _Harvey P. Dale_, Jun 28 2011 *)
%o A105450 (PARI) a(n)=n*(n^5+15*n^4+85*n^3+465*n^2+1354*n+2400)/720 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A105450 Cf. A051743, A006027.
%K A105450 nonn,easy
%O A105450 0,2
%A A105450 D. G. Rogers, May 07 2005