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A130624
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Binomial transform of A101000.
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2
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0, 1, 5, 12, 23, 43, 84, 169, 341, 684, 1367, 2731, 5460, 10921, 21845, 43692, 87383, 174763, 349524, 699049, 1398101, 2796204, 5592407, 11184811, 22369620, 44739241, 89478485, 178956972, 357913943, 715827883, 1431655764, 2863311529
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(0) = 0, a(1) = 1, a(2) = 5; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
a(0) = 0; a(n+1) = 2*a(n) + A119910(n).
G.f.: x*(1+2*x)/((1-2*x)*(1-x+x^2)).
a(n)=-(2/3)*[1/2-(1/2)*I*sqrt(3)]^n-(2/3)*[1/2+(1/2)*I*sqrt(3)]^n+(4/3)*2^n-(1/3)*I*[1/2-(1 /2)*I*sqrt(3)]^n*sqrt(3)+(1/3)*I*[1/2+(1/2)*I*sqrt(3)]^n*sqrt(3), with n>=0 and I=sqrt(-1) [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 06 2008]
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PROG
| (PARI) {m=32; v=concat([0, 1, 5], vector(m-3)); for(n=4, m, v[n]=3*v[n-1]-3*v[n-2]+2*v[n-3]); v} /* Klaus Brockhaus, Jun 21 2007 */
(MAGMA) m:=32; S:=[ [0, 1, 3][ (n-1) mod 3 +1 ]: n in [1..m] ]; [ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; /* Klaus Brockhaus, Jun 21 2007 */
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CROSSREFS
| Cf. A101000, A119910, A130625 (first differences), A130626 (second differences).
Sequence in context: A172295 A126573 A000327 * A066869 A023172 A100479
Adjacent sequences: A130621 A130622 A130623 * A130625 A130626 A130627
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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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