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A035038
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2^n - C(n,0)- ... - C(n,5).
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14
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 24 2010: (Start)
Starting with "1" equals the eigensequence of a triangle with A000579 =
binomial C(n,6) = (1, 7, 28, 84, 210,...) as the left column and the rest 1's. (End)
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REFERENCES
| J. Eckhoff, Der Satz von Radon in konvexen Productstrukturen II, Monat. f. Math., 73 (1969), 7-30.
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FORMULA
| G.f. : x^6/((1-2x)(1-x)^6); a(n)=sum{k=0..n, C(n, k+6)} = sum{k=6..n, C(n, k)}; a(n)=2a(n-1)+C(n-1, 5). - Paul Barry (pbarry(AT)wit.ie), Aug 23 2004
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MAPLE
| (Maple) 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] ; seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 05 2008]
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MATHEMATICA
| a=1; lst={}; s1=s2=s3=s4=s5=s6=0; Do[s1+=a; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; AppendTo[lst, s6]; a=a*2, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 10 2009]
Table[Sum[ Binomial[n + 6, k + 6], {k, 0, n}], {n, -6, 24}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
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CROSSREFS
| Cf. A000079, A000225, A000295, A002663, A002664, A035039-A035042.
Sequence in context: A001780 A053296 A055799 * A111645 A128246 A204076
Adjacent sequences: A035035 A035036 A035037 * A035039 A035040 A035041
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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