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%I #22 Sep 08 2022 08:45:44
%S 9,19,40,84,176,368,768,1600,3328,6912,14336,29696,61440,126976,
%T 262144,540672,1114112,2293760,4718592,9699328,19922944,40894464,
%U 83886080,171966464,352321536,721420288,1476395008,3019898880
%N a(0)=9, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
%C Diagonal of triangles A062111, A152920.
%H G. C. Greubel, <a href="/A159697/b159697.txt">Table of n, a(n) for n = 0..3300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4).
%F a(n) = Sum_{k=0..n} (k+9)*binomial(n,k).
%F From _R. J. Mathar_, Apr 20 2009: (Start)
%F a(n) = (18+n)*2^(n-1).
%F a(n) = 4*a(n-1) - 4*a(n-2).
%F G.f.: (9-17*x)/(1-2*x)^2. (End)
%F a(0)=9, a(1)=19, a(n) = 4*a(n-1) - 4*a(n-2). - _Harvey P. Dale_, Mar 24 2013
%F a(n) = 2*A079862(n-10). - _Michel Marcus_, Sep 29 2015
%F E.g.f.: (x+9)*exp(2*x). - _G. C. Greubel_, Jun 02 2018
%e a(0)=9, a(1) = 2*9 + 1 = 19, a(2) = 2*19 + 2 = 40, a(3) = 2*40 + 4 = 84, a(4) = 2*84 + 8 = 176, ...
%t RecurrenceTable[{a[0]==9,a[n]==2a[n-1]+2^(n-1)},a,{n,30}] (* or *) LinearRecurrence[{4,-4},{9,19},30] (* _Harvey P. Dale_, Mar 24 2013 *)
%o (PARI) Vec((9-17*x)/(1-2*x)^2 + O(x^40)) \\ _Michel Marcus_, Sep 29 2015
%o (Magma) I:=[9,19]; [n le 2 select I[n] else 4*Self(n-1) - 4*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jun 02 2018
%Y Cf. A000079, A001787, A001792, A045623, A045891, A034007, A111297, A159694, A159695, A159696.
%K easy,nonn
%O 0,1
%A _Philippe Deléham_, Apr 20 2009
%E More terms from _Vincenzo Librandi_, Apr 30 2009
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