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Search: id:A081335
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| 1, 4, 20, 112, 656, 3904, 23360, 140032, 839936, 5039104, 30233600, 181399552, 1088393216, 6530351104, 39182090240, 235092508672, 1410554986496, 8463329787904, 50779978465280, 304679870267392, 1828079220555776
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OFFSET
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0,2
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COMMENT
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Binomial transform of A034478. 4th binomial transform of (1,0,4,0,16,0,64,....). Case k=4 of the family of recurrences a(n)=2k*a(n-1)-(k^2-4)*a(n-2), a(0)=1,a(1)=k.
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FORMULA
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a(n)=(6^n+2^n)/2 a(n)=8a(n-1)-12a(n-2), a(0)=1, a(1)=4. G.f.: (1-4x)/((1-2x)(1-6x)). E.g.f. exp(4x)cosh(2x).
a(n)=sum{k=0..floor(n/2), C(n, 2k)4^(n-k)}=sum{k=0..n, C(n, k)4^(n-k/2)(1+(-1)^k)/2} - Paul Barry (pbarry(AT)wit.ie), Nov 22 2003
a(n) = Sum_{k, 0<=k<=n}4^k*A098158(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2006
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CROSSREFS
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Cf. A081336.
Sequence in context: A026156 A025183 A014523 this_sequence A136783 A080609 A003645
Adjacent sequences: A081332 A081333 A081334 this_sequence A081336 A081337 A081338
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 18 2003
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