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A187919
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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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0
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3, 32, 256, 1912, 13989, 101656, 737078, 5340368, 38683143, 280179632, 2029268236, 14697327880, 106447627113, 770962306792, 5583803916866, 40441487719712, 292903169916939, 2121392429130176, 15364483152682648, 111279430895716888, 805956934031993133, 5837256482937956152, 42277151305568313806, 306198216183841310960, 2217683658862794974223
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OFFSET
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1,1
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COMMENTS
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Arises in the study of ternary strings.
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REFERENCES
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R. P. Grimaldi, Ternary strings with no consecutive 0's and no consecutive 1's, Congressus Numerantium, 205 (2011), 129-149. (See val_n.)
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LINKS
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FORMULA
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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
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MATHEMATICA
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LinearRecurrence[{8, -2, -24, -9}, {3, 32, 256, 1912}, 30] (* Harvey P. Dale, Feb 02 2020 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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