OFFSET
0,2
COMMENTS
It appears that the (unsigned) sequence is identical to its 7th-order absolute difference. - John W. Layman, Oct 02 2003
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (-7, -21, -35, -35, -21, -7).
FORMULA
a(n) = (-1)^n * Sum_{k=0..floor(n/7)} (-1)^k * binomial(n+6,7*k+6). - Seiichi Manyama, Mar 21 2019
MATHEMATICA
LinearRecurrence[{-7, -21, -35, -35, -21, -7}, {1, -7, 28, -84, 210, -462}, 35] (* Ray Chandler, Sep 23 2015 *)
PROG
(PARI) Vec(1/((1+x)^7-x^7)+O(x^35)) \\ Charles R Greathouse IV, Sep 27 2012
(PARI) {a(n) = (-1)^n*sum(k=0, n\7, (-1)^k*binomial(n+6, 7*k+6))} \\ Seiichi Manyama, Mar 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( 1/((1+x)^7 - x^7) )); // G. C. Greubel, Mar 17 2019
(Sage) (1/((1+x)^7 - x^7)).series(x, 35).coefficients(x, sparse=False) # G. C. Greubel, Mar 17 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
STATUS
approved