A195673 - OEIS

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A195673

Triangle T(n,k) read by rows: T(0,0)=-2, T(1,0)=3, T(1,1)=0 and T(n,k) = T(n-1,k)-T(n-2,k-2) otherwise.

-2, 3, 0, 3, 0, 2, 3, 0, -1, 0, 3, 0, -4, 0, -2, 3, 0, -7, 0, -1, 0, 3, 0, -10, 0, 3, 0, 2, 3, 0, -13, 0, 10, 0, 3, 0, 3, 0, -16, 0, 20, 0, 0, 0, -2, 3, 0, -19, 0, 33, 0, -10, 0, -5, 0, 3, 0, -22, 0, 49, 0, -30, 0, -5, 0, 2, 3, 0, -25, 0, 68

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OFFSET

0,1

COMMENTS

Obviously T(n,k) = 0 for all odd k.

Conjecture: The polynomials p(n,x) = sum_{k=0..n} T(n,k)*x^(n-k) based on this simple recurrence for other initial constant values of T(0,0)=p and T(1,0)=q are related to the S-polynomials of A053119: p(n,x,p+1,q+1)-p(n,x,p,q) = S(n,x).

LINKS

Table of n, a(n) for n=0..70.

EXAMPLE

-2;

3, 0;

3, 0, 2;

3, 0, -1, 0;

3, 0, -4, 0, -2;

3, 0, -7, 0, -1, 0;

3, 0, -10, 0, 3, 0, 2;

3, 0, -13, 0, 10, 0, 3, 0.

CROSSREFS

Cf. A195662, A192011 (p=-1, q=2), A135929 (p=-2, q=1).

Sequence in context: A354077 A059283 A160202 * A339674 A241070 A128621

Adjacent sequences: A195670 A195671 A195672 * A195674 A195675 A195676

KEYWORD

sign,easy,tabl

AUTHOR

Paul Curtz, Sep 23 2011

STATUS

approved