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A104063 Triangle read by rows: T(n,k) = (-1)^k*3^(n-1-2k)*binomial(n-k,k)*(4n-5k)/(n-k) (0 <= k <= floor(n/2), n >= 1). 0

%I

%S 1,4,12,-1,36,-7,108,-33,1,324,-135,10,972,-513,63,-1,2916,-1863,324,

%T -13,8748,-6561,1485,-102,1,26244,-22599,6318,-630,16,78732,-76545,

%U 25515,-3375,150,-1,236196,-255879,99144,-16443,1080,-19,708588,-846369,373977,-74844,6615,-207,1

%N Triangle read by rows: T(n,k) = (-1)^k*3^(n-1-2k)*binomial(n-k,k)*(4n-5k)/(n-k) (0 <= k <= floor(n/2), n >= 1).

%H P. Filipponi, <a href="https://www.fq.math.ca/Scanned/36-1/filipponi1.pdf">Combinatorial expressions for Lucas numbers</a>, The Fibonacci Quarterly, 36, 1998, 63-65.

%H A. Panholzer and H. Prodinger, <a href="https://www.fq.math.ca/Scanned/38-2/panholzer.pdf">Two proofs of Filipponi's formula for odd-subscripted Lucas numbers</a>, The Fibonacci Quarterly, 38, 2000, 165-166.

%p T:=proc(n,k) if k=0 and n=0 then 1 elif k<=floor(n/2) then (-1)^k*binomial(n-k,k)*3^(n-1-2*k)*(4*n-5*k)/(n-k) else 0 fi end: for n from 0 to 12 do seq(T(n,k),k=0..floor(n/2)) od;

%Y Row sums yield the odd-indexed Lucas numbers (A002878).

%K sign,tabf

%O 0,2

%A _Emeric Deutsch_, Mar 02 2005

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Last modified May 27 03:13 EDT 2022. Contains 354093 sequences. (Running on oeis4.)