A131090 First differences of A131666.

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

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

Table of n, a(n) for n=0..34.

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