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 A130625 First differences of A130624. 3
 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; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = A130624(n+1) - A130624(n). LINKS Index entries for linear recurrences with constant coefficients, signature (3,-3,2). 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, 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, Jun 12 2008 MATHEMATICA LinearRecurrence[{3, -3, 2}, {1, 4, 7}, 40] (* Harvey P. Dale, Apr 27 2015 *) 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 */ CROSSREFS Cf. A130624, A130626 (second differences). Sequence in context: A083839 A091176 A002974 * A104102 A074705 A288111 Adjacent sequences:  A130622 A130623 A130624 * A130626 A130627 A130628 KEYWORD nonn AUTHOR Paul Curtz, Jun 18 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, Jun 21 2007 STATUS approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)