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A093967
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a(n) = n * Pell(n).
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13
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0, 1, 4, 15, 48, 145, 420, 1183, 3264, 8865, 23780, 63151, 166320, 434993, 1130948, 2925375, 7533312, 19323713, 49395780, 125877071, 319888560, 810893265, 2050891876, 5176349663, 13040153280, 32793453025, 82337215012, 206424991215
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: x*(1+x^2)/(1 - 2*x - x^2)^2;
a(n) = n*((1+sqrt(2))^n - (1-sqrt(2))^n)/(2*sqrt(2));
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MAPLE
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MATHEMATICA
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LinearRecurrence[{4, -2, -4, -1}, {0, 1, 4, 15}, 30] (* Vincenzo Librandi, Dec 20 2015 *)
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PROG
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(PARI) { default(realprecision, 100); s=sqrt(2); for (n=0, 100, a=n*round(((1+s)^n-(1-s)^n)/(2*s)); write("b093967.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 17 2009
(Magma) I:=[0, 1, 4, 15]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)-4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 20 2015
(Sage) [n*lucas_number1(n, 2, -1) for n in (0..30)] # G. C. Greubel, Dec 28 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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