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A097788
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a(n)=4a(n-1)+C(n+3,3),n>0, a(0)=1.
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5
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1, 8, 42, 188, 787, 3204, 12900, 51720, 207045, 828400, 3313886, 13255908, 53024087, 212096908, 848388312, 3393554064, 13574217225, 54296870040, 217187481490, 868749927500, 3474999711771, 13899998849108, 55599995398732
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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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G.f.: 1/((1-4x)(1-x)^4); a(n)=4^(n+4)/81-(9n^3+90n^2+303n+350)/162; a(n)=sum{k=0..n, binomial(n+4, k+4)3^k}.
a(0)=1, a(1)=8, a(2)=42, a(3)=188, a(4)=787, a(n)=8*a(n-1)- 22*a(n-2)+ 28*a(n-3)- 17*a(n-4)+4*a(n-5). - Harvey P. Dale, May 04 2014
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MATHEMATICA
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RecurrenceTable[{a[0]==1, a[n]==4a[n-1]+Binomial[n+3, 3]}, a, {n, 30}] (* or *) LinearRecurrence[{8, -22, 28, -17, 4}, {1, 8, 42, 188, 787}, 30] (* Harvey P. Dale, May 04 2014 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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