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A130626
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Second differences of A130624.
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2
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3, 3, 4, 9, 21, 44, 87, 171, 340, 681, 1365, 2732, 5463, 10923, 21844, 43689, 87381, 174764, 349527, 699051, 1398100, 2796201, 5592405, 11184812, 22369623, 44739243, 89478484, 178956969, 357913941, 715827884, 1431655767, 2863311531
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| First differences of A130625: a(n) = A130625(n+1) - A130625(n).
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FORMULA
| G.f.: (3-6*x+4*x^2)/((1-2*x)*(1-x+x^2)).
a(n)=3a(n-1)-3a(n-2)+2a(n-3). - Paul Curtz (bpcrtz(AT)free.fr), Apr 24 2008
a(n)=(5/6)*[1/2-(1/2)*I*sqrt(3)]^n+(5/6)*[1/2+(1/2)*I*sqrt(3)]^n+(4/3)*2^n-(1/6)*I*[1/2-(1 /2)*I*sqrt(3)]^n*sqrt(3)+(1/6)*I*[1/2+(1/2)*I*sqrt(3)]^n*sqrt(3), with n>=0 and I=sqrt(-1) - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 12 2008
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PROG
| (MAGMA) m:=34; S:=[ [0, 1, 3][ (n-1) mod 3 +1 ]: n in [1..m] ]; T:=[ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; U:=[ T[n+1]-T[n]: n in[1..m-1] ]; [ U[n+1]-U[n]: n in[1..m-2] ]; /* Klaus Brockhaus, Jun 21 2007 */
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CROSSREFS
| Cf. A130624, A130625.
Sequence in context: A022598 A107635 A132319 * A175796 A115284 A202869
Adjacent sequences: A130623 A130624 A130625 * A130627 A130628 A130629
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KEYWORD
| nonn
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jun 18 2007
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EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 21 2007
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