

A104063


Triangle read by rows: T(n,k) = (1)^k*3^(n12k)*binomial(nk,k)*(4n5k)/(nk) (0 <= k <= floor(n/2), n >= 1).


0



1, 4, 12, 1, 36, 7, 108, 33, 1, 324, 135, 10, 972, 513, 63, 1, 2916, 1863, 324, 13, 8748, 6561, 1485, 102, 1, 26244, 22599, 6318, 630, 16, 78732, 76545, 25515, 3375, 150, 1, 236196, 255879, 99144, 16443, 1080, 19, 708588, 846369, 373977, 74844, 6615, 207, 1
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..48.
P. Filipponi, Combinatorial expressions for Lucas numbers, The Fibonacci Quarterly, 36, 1998, 6365.
A. Panholzer and H. Prodinger, Two proofs of Filipponi's formula for oddsubscripted Lucas numbers, The Fibonacci Quarterly, 38, 2000, 165166.


MAPLE

T:=proc(n, k) if k=0 and n=0 then 1 elif k<=floor(n/2) then (1)^k*binomial(nk, k)*3^(n12*k)*(4*n5*k)/(nk) else 0 fi end: for n from 0 to 12 do seq(T(n, k), k=0..floor(n/2)) od;


CROSSREFS

Row sums yield the oddindexed Lucas numbers (A002878).
Sequence in context: A073902 A144207 A016487 * A260430 A243347 A317555
Adjacent sequences: A104060 A104061 A104062 * A104064 A104065 A104066


KEYWORD

sign,tabf,changed


AUTHOR

Emeric Deutsch, Mar 02 2005


STATUS

approved



