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 A131090 First differences of A131666. 5
 0, 1, 0, 1, 1, 4, 7, 15, 28, 57, 113, 228, 455, 911, 1820, 3641, 7281, 14564, 29127, 58255, 116508, 233017, 466033, 932068, 1864135, 3728271, 7456540, 14913081, 29826161, 59652324, 119304647, 238609295, 477218588, 954437177, 1908874353 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The first differences b(n)=a(n+1)-a(n) obey the recurrence b(n+1)-2b(n) = (-3,3,-2,3,-3,2), continued with period 6. The 2nd differences c(n)=b(n+1)-b(n) obey the recurrence c(n+1)-2c(n) = (6,-5,5,-6,5,-5), periodically continued with period 6. The hexaperiodic coefficients in these recurrences for A113405, A131666 and their higher order differences define a table, 0, 0, 1, 0, 0, -1 <- A113405 0, 1, -1, 0, -1, 1 <- A131666 1, -2, 1, -1, 2, -1 <- a(n) -3, 3, -2, 3, -3, 2 <- b(n) 6, -5, 5, -6, 5, -5 <- c(n) -11,10,-11, 11,-10, 11 21,-21,22,-21, 21,-22 ... in which the first three columns are A024495, A131708 and A024493, multiplied by a checkerboard pattern of signs. LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2). FORMULA a(n) = A131666(n+1)-A131666(n). a(n+1)-2a(n) = A131556(n), a sequence with period length 6. G.f.: -(x-1)^2*x / ((x+1)*(2*x-1)*(x^2-x+1)). - Colin Barker, Mar 04 2013 MATHEMATICA LinearRecurrence[{2, 0, -1, 2}, {0, 1, 0, 1}, 40] (* Harvey P. Dale, Jan 15 2016 *) CROSSREFS Sequence in context: A027419 A301204 A116969 * A178615 A131935 A119749 Adjacent sequences:  A131087 A131088 A131089 * A131091 A131092 A131093 KEYWORD easy,nonn AUTHOR Paul Curtz, Sep 24 2007 EXTENSIONS Edited by R. J. Mathar, Jun 28 2008 STATUS approved

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Last modified June 19 05:18 EDT 2021. Contains 345125 sequences. (Running on oeis4.)