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A048492
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a(n) = ( 8*(2^n) - n^2 - 3*n - 6 )/2.
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4
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1, 3, 8, 20, 47, 105, 226, 474, 977, 1991, 4028, 8112, 16291, 32661, 65414, 130934, 261989, 524115, 1048384, 2096940, 4194071, 8388353, 16776938, 33554130, 67108537, 134217375, 268435076, 536870504, 1073741387, 2147483181
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(0) = 1; a(n) = a(n-1) + 2^(n+1) - (n+1) for n > 0. - Klaus Brockhaus, Oct 13 2008
a(n) = (-2+2^(2+n)-1/2*(1+n)*(2+n)).
a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4).
G.f.: (2*x^2-2*x+1) / ((x-1)^3*(2*x-1)).
(End)
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MATHEMATICA
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Table[(8*2^n-n^2-3n-6)/2, {n, 0, 30}]
LinearRecurrence[{5, -9, 7, -2}, {1, 3, 8, 20}, 40] (* Harvey P. Dale, Aug 28 2019 *)
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PROG
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(ARIBAS) a:=0; for n:=1 to 30 do a:=a+2**n-n; write(a, ", "); end; # Klaus Brockhaus, Oct 13 2008
(Magma) [( 8*(2^n) -n^2 -3*n -6 )/2: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011
(PARI) Vec((2*x^2-2*x+1) / ((x-1)^3*(2*x-1)) + O(x^100)) \\ Colin Barker, Oct 27 2014
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CROSSREFS
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a(n)=T(0, n)+T(1, n-1)+...+T(n, 0), array T given by A048483.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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