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A130625
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First differences of A130624.
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3
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1, 4, 7, 11, 20, 41, 85, 172, 343, 683, 1364, 2729, 5461, 10924, 21847, 43691, 87380, 174761, 349525, 699052, 1398103, 2796203, 5592404, 11184809, 22369621, 44739244, 89478487, 178956971, 357913940, 715827881, 1431655765, 2863311532
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = A130624(n+1) - A130624(n).
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FORMULA
| G.f.: (1-x)*(1+2*x)/((1-2*x)*(1-x+x^2)).
a(n)=3a(n-1)-3a(n-2)+2a(n-3). Sequence is identical to its third differences. Binomial transform of 1, 3, 0. - Paul Curtz (bpcrtz(AT)free.fr), Nov 23 2007
a(n)=-(1/6)*[1/2-(1/2)*I*sqrt(3)]^n-(1/6)*[1/2+(1/2)*I*sqrt(3)]^n+(4/3)*2^n+(1/2)*I*[1/2-(1 /2)*I*sqrt(3)]^n*sqrt(3)-(1/2)*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:=33; 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] ]; [ T[n+1]-T[n]: n in[1..m-1] ]; /* Klaus Brockhaus, Jun 21 2007 */
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CROSSREFS
| Cf. A130624, A130626 (second differences).
Sequence in context: A083839 A091176 A002974 * A104102 A074705 A179165
Adjacent sequences: A130622 A130623 A130624 * A130626 A130627 A130628
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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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