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A094388
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Expansion of (1- 2x - x^2)/((1-x)*(1-3x)).
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2
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1, 2, 4, 10, 28, 82, 244, 730, 2188, 6562, 19684, 59050, 177148, 531442, 1594324, 4782970, 14348908, 43046722, 129140164, 387420490, 1162261468, 3486784402, 10460353204, 31381059610, 94143178828, 282429536482, 847288609444
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OFFSET
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0,2
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COMMENTS
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Binomial transform of 0^n + A001045(n).
Form an array with the first row and column containing all 1's: m(n,1)=m(1,n)=1 for n=1,2,3,... An interior term m(i,j) is the sum of all preceding terms in row(i) and all preceding terms in column(j): m(i,j) = Sum_{k=1..j-1} m(i,k) + Sum_{l=1..i-1} m(l,j). The sum of the terms in each antidiagonal will reproduce the terms in this sequence beginning at a(0).
The upper left corner of the array begins
1 1 1 1 1 ...
1 2 4 8 16 ...
1 4 10 24 56 ...
1 8 24 66 172 ...
1 16 56 172 490 ...
...
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LINKS
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FORMULA
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a(n) = 3^n/3 - 0^n/3 + 1; a(n+1) = 2*A007051(n); a(n+1) - 1 = 3^n.
G.f.: G(0), where G(k)= 1 + 3^k*x/(1 - x/(x + 3^k*x/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 26 2013
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MATHEMATICA
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CoefficientList[Series[(1-2x-x^2)/((1-x)(1-3x)), {x, 0, 30}], x] (* Harvey P. Dale, May 20 2011 *)
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PROG
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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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