A126030 Riordan array (1/(1+x^3),x/(1+x^3)).

1, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, -2, 0, 0, 1, 0, 0, -3, 0, 0, 1, 1, 0, 0, -4, 0, 0, 1, 0, 3, 0, 0, -5, 0, 0, 1, 0, 0, 6, 0, 0, -6, 0, 0, 1, -1, 0, 0, 10, 0, 0, -7, 0, 0, 1, 0, -4, 0, 0, 15, 0, 0

Offset

0,12

Comments

Inverse is A111373. Row sums are A050935(n+2). Diagonal sums are an alternating sign version of A000931(n+3) with g.f. 1/(1-x^2+x^3).

Links

Table of n, a(n) for n=0..61.

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3

Formula

Number triangle T(n,k)=C(k+(n-k)/3,(n-k)/3)*(-1)^(n-k)*(2*cos(2*pi*(n-k)/3)+1)/3

Example

Triangle begins
.1,
.0, 1,
.0, 0, 1,
.-1, 0, 0, 1,
.0, -2, 0, 0, 1,
.0, 0, -3, 0, 0, 1,
.1, 0, 0, -4, 0, 0, 1,
.0, 3, 0, 0, -5, 0, 0, 1,
.0, 0, 6, 0, 0, -6, 0, 0, 1,
.-1, 0, 0, 10, 0, 0, -7, 0, 0, 1,
.0, -4, 0, 0, 15, 0, 0, -8, 0, 0, 1

Crossrefs

Sequence in context: A363805 A212193 A253189 * A111373 A336757 A116376

Adjacent sequences: A126027 A126028 A126029 * A126031 A126032 A126033

Keyword

easy,sign,tabl

Author

Paul Barry, Dec 15 2006

Status

approved