A140874 Triangle T(n,k) = binomial(n,k+2)-2*binomial(n,k+1)-binomial(n,k) read by rows, 0<=k<=n-2, n>=2.

-4, -4, -8, -3, -12, -13, -1, -15, -25, -19, 2, -16, -40, -44, -26, 6, -14, -56, -84, -70, -34, 11, -8, -70, -140, -154, -104, -43, 17, 3, -78, -210, -294, -258, -147, -53, 24, 20, -75, -288, -504, -552, -405, -200, -64

Offset

2,1

Comments

Row sums are 4-2^(n+1).

Links

Table of n, a(n) for n=2..46.

Example

-4;
-4, -8;
-3, -12, -13;
-1, -15, -25, -19;
2, -16, -40, -44, -26;
6, -14, -56, -84, -70, -34;
11, -8, -70, -140, -154, -104, -43;
17, 3, -78, -210, -294, -258, -147, -53;
24, 20, -75, -288, -504, -552, -405, -200, -64;

Mathematica

Clear[T, D2, x, a, n, m] T[n_, m_] := Binomial[n, m] D2[n_, m_] := If[m + 2 <= n, T[n, m + 2] - 2*T[n, m + 1] - T[n, m], {} ]; a = Table[Flatten[Table[D2[n, m], {m, 0, n}]], {n, 0, 10}]; Flatten[a]

Crossrefs

Cf. A007318.

Sequence in context: A137797 A358561 A176295 * A355234 A021227 A349778

Adjacent sequences: A140871 A140872 A140873 * A140875 A140876 A140877

Keyword

easy,tabl,sign

Author

Roger L. Bagula and Gary W. Adamson, Jul 21 2008

Extensions

Sign in definition corrected by R. J. Mathar, Sep 09 2013

Status

approved