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A016290
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Expansion of 1/((1-2x)(1-4x)(1-8x)).
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5
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1, 14, 140, 1240, 10416, 85344, 690880, 5559680, 44608256, 357389824, 2861214720, 22898104320, 183218384896, 1465881288704, 11727587164160, 93822844764160, 750591347982336, 6004765143465984, 48038258586419200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Index to sequences with linear recurrences with constant coefficients, signature (14,-56,64).
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FORMULA
| Difference of Gaussian binomial coefficients [ n+1, 3 ]-[ n, 3 ] (n >= 2).
a(n)=(2^n-6*4^n+8*8^n)/3 - Jim Buddenhagen (jbuddenh(AT)gmail.com), Dec 14 2003
a(n)=sum{0<=i,j,k,<=n, i+j+k=n, 2^i*4^j*8^k}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 25 2007
Contribution from Vincenzo Librandi, Mar 15 2011: (Start)
a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3), n>=3.
a(n) = 12*a(n-1) - 32*a(n-2) + 2^n, a(0)=1, a(1)=14.
(End)
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MAPLE
| [ seq(GBC(n+1, 3, 2)-GBC(n, 3, 2), n=2..30) ]; # produces A016290 (cf. A006516).
seq((2^n-6*4^n+8*8^n)/3, n=1..20);
seq(binomial(2^n, 3)/4, n=2..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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MATHEMATICA
| CoefficientList[Series[1/((1-2x)(1-4x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{14, -56, 64}, {1, 14, 140}, 30] (* From Harvey P. Dale, Jul 23 2011 *)
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CROSSREFS
| Cf. A006516.
Sequence in context: A021044 A121034 A125402 * A003457 A016241 A131583
Adjacent sequences: A016287 A016288 A016289 * A016291 A016292 A016293
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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