# [seqfan] Re: Convolve tribonacci with trinomials = A099464?

Richard Mathar mathar at strw.leidenuniv.nl
Mon Oct 18 23:16:38 CEST 2010

```http://list.seqfan.eu/pipermail/seqfan/2010-October/006245.html says

mh> The analogy works in all variations:
mh>
mh>   Sum {k=0.. (m-1) n} (m-ibonacci(k+b) * m-inomial(n,k) ) = m-ibonacci(m*n+b)

The first 5 cases, m=3..7, can be rephrased in OEIS speak, I think. For m=8,
there is a lack of the 8-inomial array (marked by Axxxxxx):

%F A000073 sum_{k=0..2*n} A000073(k+b)*A027907(n,k) = A000073(3*n+b), b>=0 (see A099464, A074581).

%F A000078 sum_{k=0..3*n} A000078(k+b)*A008287(n,k) = A000078(4*n+b), b>=0.

%F A001591 sum_{k=0..4*n} A001591(k+b)*A035343(n,k) = A001591(5*n+b), b>=0.

%F A001592 sum_{k=0..5*n} A001592(k+b)*A063260(n,k) = A001592(6*n+b), b>=0.

%F A122189 sum_{k=0..6*n} A122189(k+b)*A063265(n,k) = A122189(7*n+b), b>=0.

%F A079262 sum_{k=0..7*n} A079262(k+b)*Axxxxxx(n,k) = A079262(8*n+b), b>=0.

See also the paper
http://www.m-hikari.com/ijcms-password2008/21-24-2008/schorkIJCMS21-24-2008.pdf

```

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