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%I
%S 1,9,66,466,3267,22875,160132,1120932,7846533,54925741,384480198,
%T 2691361398,18839529799,131876708607,923136960264,6461958721864,
%U 45233711053065,316635977371473,2216451841600330
%N a(1)=1; for n > 1, a(n) = 7*a(n-1) + n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-15,7).
%F a(n) = (7^(n+1) - 6*n - 7)/36. - _Rolf Pleisch_, Oct 19 2010
%F a(1)=1, a(2)=9, a(3)=66; for n > 3, a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). - _Harvey P. Dale_, Jul 22 2013
%F a(n) = Sum_{i=0..n-1} 6^i*binomial(n+1,n-1-i). - _Bruno Berselli_, Nov 13 2015
%e For n=5, a(5) = 1*15 + 6*20 + 6^2*15 + 6^3*6 + 6^4*1 = 3267. - _Bruno Berselli_, Nov 13 2015
%p a:=n->sum((7^(n-j)-1)/6,j=0..n): seq(a(n), n=1..19); # _Zerinvary Lajos_, Jan 15 2007
%t a[1] = 1; a[n_] := 7*a[n-1]+n; Table[a[n], {n, 10}] (* _Zak Seidov_, Feb 06 2011 *)
%t LinearRecurrence[{9, -15, 7}, {1, 9, 66}, 30] (* _Harvey P. Dale_, Jul 22 2013 *)
%Y Cf. A000400, A104712.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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