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A035038
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a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,5).
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19
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0, 0, 0, 0, 0, 0, 1, 8, 37, 130, 386, 1024, 2510, 5812, 12911, 27824, 58651, 121670, 249528, 507624, 1026876, 2069256, 4158861, 8344056, 16721761, 33486026, 67025182, 134116144, 268313018, 536724316, 1073567387, 2147277280, 4294724471, 8589650318, 17179537972
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OFFSET
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0,8
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COMMENTS
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Starting with "1", equals the eigensequence of a triangle with A000579 = binomial(n,6) = (1, 7, 28, 84, 210, ...) as the left column and the rest 1's. - Gary W. Adamson, Jul 24 2010
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LINKS
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FORMULA
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G.f.: x^6/((1-2*x)*(1-x)^6).
a(n) = Sum_{k=0..n} C(n, k+6) = Sum_{k=6..n} C(n, k).
a(n) = 2*a(n-1) + C(n-1, 5). (End)
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MAPLE
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a:= n-> (Matrix(7, (i, j)-> if (i=j-1) then 1 elif j=1 then [8, -27, 50, -55, 36, -13, 2][i] else 0 fi)^(n))[1, 7]:
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MATHEMATICA
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Table[Sum[Binomial[n, k+6], {k, 0, n}], {n, 0, 30}] (* Zerinvary Lajos, Jul 08 2009 *)
Table[2^n-Total[Binomial[n, Range[0, 5]]], {n, 0, 40}] (* Harvey P. Dale, Oct 24 2017 *)
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PROG
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(Haskell)
a035038 n = a035038_list !! n
a035038_list = map (sum . drop 6) a007318_tabl
(Magma) [n le 5 select 0 else (&+[Binomial(n, j): j in [6..n]]): n in [0..50]]; // G. C. Greubel, Mar 20 2023
(SageMath) [sum(binomial(n, j) for j in range(6, n+1)) for n in range(51)] # G. C. Greubel, Mar 20 2023
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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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