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A008999
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a(n) = 2*a(n-1) + a(n-4).
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11
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1, 2, 4, 8, 17, 36, 76, 160, 337, 710, 1496, 3152, 6641, 13992, 29480, 62112, 130865, 275722, 580924, 1223960, 2578785, 5433292, 11447508, 24118976, 50816737, 107066766, 225581040, 475281056, 1001378849
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{m=0..n} Sum_{j=0..(n-m)/3} binomial(n-m+(-3)*j,j)*binomial(n-3*j,m). - Vladimir Kruchinin, May 23 2011
O.g.f.: exp( Sum {n>=1} ( (1 + sqrt(1 + x^2))^n + (1 - sqrt(1 + x^2))^n ) * x^n/n ). Cf. A008998. - Peter Bala, Dec 22 2014
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MAPLE
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MATHEMATICA
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LinearRecurrence[{2, 0, 0, 1}, {1, 2, 4, 8}, 40] (* Harvey P. Dale, May 09 2012 *)
CoefficientList[Series[1/(1-2x-x^4), {x, 0, 40}], x] (* Vincenzo Librandi, May 09 2012 *)
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PROG
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(Maxima) a(n):=sum(sum(binomial(n-m+(-3)*j, j)*binomial(n-3*j, m), j, 0, (n-m)/3), m, 0, n); /* Vladimir Kruchinin, May 23 2011 */
(Magma) I:=[1, 2, 4, 8]; [n le 4 select I[n] else 2*Self(n-1)+Self(n-4): n in [1..40]]; // Vincenzo Librandi, May 09 2012
(PARI) my(x='x+O('x^40)); Vec(1/(1-2*x-x^4)) \\ G. C. Greubel, Jun 12 2019
(Sage) (1/(1-2*x-x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 12 2019
(GAP) a:=[1, 2, 4, 8];; for n in [5..40] do a[n]:=2*a[n-1]+a[n-4]; od; a; # G. C. Greubel, Jun 12 2019
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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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