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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

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

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