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A063782
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a(0) = 1, a(1) = 3; for n>1, a(n) = 2*a(n-1) + 4*a(n-2).
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3
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1, 3, 10, 32, 104, 336, 1088, 3520, 11392, 36864, 119296, 386048, 1249280, 4042752, 13082624, 42336256, 137003008, 443351040, 1434714112, 4642832384, 15024521216, 48620371968, 157338828800, 509159145472, 1647673606144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Ratio of successive terms approaches sqrt(5) + 1.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
| For n >= 1, a(n) = 2^(n-1)*Fibonacci(n+3). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 25 2003
G.f. (1 + x)/(1 - 2x - 4x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 06 2010]
Equals INVERT transform of A006138 and INVERTi transform of A179606. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2010
a(n)=(1/2)*(1+sqrt(5))^n+(1/5)*(1+sqrt(5))^n*sqrt(5)-(1/5)*sqrt(5)*(1-sqrt(5))^n+1/2*(1 -sqrt(5))^n [From Alexander R. Povolotsky (pevnev(AT)juno.com), Aug 15 2010]
G.f.: -x*(3+4*x)/(-1+2*x+4*x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 06 2010]
a(n) = f(n) + f(n-1), where f() = A063727.
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EXAMPLE
| As the INVERT transform of A006138, (1, 2, 5, 11, 26, 59,...); a(4) = 104 = (26, 11, 5, 2, 1) dot (1, 1, 3, 10, 32) = (26 + 11 + 15 + 20 + 32).
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MAPLE
| a := proc(n) option remember: if n=0 then RETURN(1) fi: if n=1 then RETURN(2) fi: 2*a(n-1) + 4*a(n-2); end: for n from 1 to 50 do printf(`%d, `, a(n)+a(n-1)) od:
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 5}, {1, 1}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 20 2010]
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PROG
| (PARI) { for (n=0, 200, if (n>1, a=2*a1 + 4*a2; a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); if (n, write("b063782.txt", n, " ", a + a2)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 31 2009]
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CROSSREFS
| Cf. A006138
Sequence in context: A134377 A077826 A033505 * A071718 A134952 A184436
Adjacent sequences: A063779 A063780 A063781 * A063783 A063784 A063785
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KEYWORD
| nonn
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AUTHOR
| Klaus E. Kastberg (kastberg(AT)hotkey.net.au), Aug 17 2001
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 25 2001
Edited (new offset, new initial term, etc.) by N. J. A. Sloane, Aug 19 2010
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