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A100206 Row sums of Clark's triangle A046902.

%I A100206 #34 Feb 16 2025 08:32:55
%S A100206 0,7,20,46,98,202,410,826,1658,3322,6650,13306,26618,53242,106490,
%T A100206 212986,425978,851962,1703930,3407866,6815738,13631482,27262970,
%U A100206 54525946,109051898,218103802,436207610,872415226,1744830458,3489660922
%N A100206 Row sums of Clark's triangle A046902.
%H A100206 Vincenzo Librandi, <a href="/A100206/b100206.txt">Table of n, a(n) for n = 0..1000</a>
%H A100206 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClarksTriangle.html">Clark's Triangle</a>.
%H A100206 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A100206 a(0)=0; for n>0, a(n) = 13*2^(n-1) - 6. - _Max Alekseyev_, May 12 2005
%F A100206 From _Chai Wah Wu_, May 28 2016: (Start)
%F A100206 a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
%F A100206 G.f.: x*(7 - x)/((1 - x )*(1 - 2*x)). (End)
%F A100206 E.g.f.: (1/2)*(13*exp(2*x) - 12*exp(x) - 1). - _G. C. Greubel_, Apr 02 2024
%e A100206 a(0) =  0.
%e A100206 a(1) =  6 +  1.
%e A100206 a(2) = 12 +  7 +  1.
%e A100206 a(3) = 18 + 19 +  8 + 1.
%e A100206 a(4) = 24 + 37 + 27 + 9 + 1.
%t A100206 Join[{0}, Table[13 2^(n-1) - 6, {n, 1, 40}]] (* _Vincenzo Librandi_, May 29 2016 *)
%t A100206 LinearRecurrence[{3,-2},{0,7,20},30] (* _Harvey P. Dale_, Jul 07 2024 *)
%o A100206 (PARI) {a(n) = if(n,13*2^(n-1)-6,0)} \\ _Max Alekseyev_, May 12 2005
%o A100206 (Magma) [0] cat [13*2^(n-1)-6: n in [1..40]]; // _Vincenzo Librandi_, May 29 2016
%o A100206 (SageMath) [(13*2^n - 12 - int(n==0))/2 for n in range(41)] # _G. C. Greubel_, Apr 02 2024
%Y A100206 Cf. A046902.
%K A100206 nonn,easy
%O A100206 0,2
%A A100206 _Jorge Coveiro_, Dec 28 2004
%E A100206 More terms from _Max Alekseyev_, May 12 2005