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A008936
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Expansion of (1 - 2*x -x^4) / (1 - 2*x)^2 in powers of x.
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1
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1, 2, 4, 8, 15, 28, 52, 96, 176, 320, 576, 1024, 1792, 3072, 5120, 8192, 12288, 16384, 16384, 0, -65536, -262144, -786432, -2097152, -5242880, -12582912, -29360128, -67108864, -150994944, -335544320, -738197504
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..30.
Index entries for linear recurrences with constant coefficients, signature (4, -4).
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FORMULA
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a(n) = 2^n for all n<4. - Michael Somos, Aug 19 2014
a(n) = 4*(a(n-1) - a(n-2)) for all n in Z except n=4. - Michael Somos, Aug 19 2014
a(n) = 2*a(n-1) - 2^(n-4) = 2^n - (n-3) * 2^(n-4) for all n>=4. - Michael Somos, Aug 19 2014
0 = a(n)*(-8*a(n+1) + 8*a(n+2) - 2*a(n+3)) + a(n+1)*(+4*a(n+1) - 4*a(n+2) + a(n+3)) for all n in Z. - Michael Somos, Aug 19 2014
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EXAMPLE
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G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 15*x^4 + 28*x^5 + 52*x^6 + 96*x^7 + 176*x^8 + ...
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MAPLE
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A008936 := proc(n) option remember; if n <= 3 then 2^n else 2*A008936(n-1)-2^(n-4); fi; end;
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MATHEMATICA
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a[ n_] := 2^n - 2^(n-4) Max[0, n-3]; (* Michael Somos, Aug 19 2014 *)
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PROG
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(PARI) {a(n) = 2^n - 2^(n-4) * max(n-3, 0)}; /* Michael Somos, 12 Jan 2000 */
(PARI) Vec((1-2*x-x^4)/(1-2*x)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
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CROSSREFS
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Sequence in context: A114833 A065617 A062065 * A320452 A073769 A008937
Adjacent sequences: A008933 A008934 A008935 * A008937 A008938 A008939
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane, Alejandro Teruel (teruel(AT)usb.ve)
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EXTENSIONS
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Better description from Michael Somos, Jan 12 2000.
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STATUS
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approved
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