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

[Mitch Harris]

The analogy works in all variations:

  Sum {k=0.. (m-1) n} (m-ibonacci(k+b) * m-inomial(n,k) ) =
m-ibonacci(m*n+b)

Surely already known (but Koushy and Vajda are not encyclopedic).
Obvious? Surely an extension of a combinatorial proof in Benjamin/Quinn.

Mitch


> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu 
> [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of David Scambler
> Sent: Sunday, October 17, 2010 10:58 PM
> To: seqfan at list.seqfan.eu
> Subject: [seqfan] Convolve tribonacci with trinomials = A099464?
> 
> Apparently,
> 
> Sum {k=0..2n} ( tribonacci(k) * trinomial(n,k) ) = 
> tribonacci(3n) = A099464.
> Already known? Obvious?
> 
> Note that A074581 also claims to be tribonacci(3n) but I 
> think it is actually tribonacci(3n+1).
> 
> A similar formula apparently applies,
> Sum {k=0..2n} ( tribonacci(k+1) * trinomial(n,k) ) = 
> tribonacci(3n+1) = A074581.
> 
> dave
> 
> 
> 
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