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a(n) = (19/28)*(3^n-1)*P(n-1)+(3/7)*(4*3^n-5)*P(n) where P() are the Pell numbers A000129.
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%I #15 Feb 02 2020 16:08:23

%S 3,32,256,1912,13989,101656,737078,5340368,38683143,280179632,

%T 2029268236,14697327880,106447627113,770962306792,5583803916866,

%U 40441487719712,292903169916939,2121392429130176,15364483152682648,111279430895716888,805956934031993133,5837256482937956152,42277151305568313806,306198216183841310960,2217683658862794974223

%N a(n) = (19/28)*(3^n-1)*P(n-1)+(3/7)*(4*3^n-5)*P(n) where P() are the Pell numbers A000129.

%C Arises in the study of ternary strings.

%D R. P. Grimaldi, Ternary strings with no consecutive 0's and no consecutive 1's, Congressus Numerantium, 205 (2011), 129-149. (See val_n.)

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-2,-24,-9).

%F G.f.: x*(6*x^2+8*x+3) / ((x^2+2*x-1)*(9*x^2+6*x-1)). - _Colin Barker_, Jul 25 2013

%t LinearRecurrence[{8,-2,-24,-9},{3,32,256,1912},30] (* _Harvey P. Dale_, Feb 02 2020 *)

%Y Cf. A000129 (Pell numbers).

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Mar 16 2011