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).

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

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, 63-65.

A. Panholzer and H. Prodinger, Two proofs of Filipponi's formula for odd-subscripted Lucas numbers, The Fibonacci Quarterly, 38, 2000, 165-166.

Maple

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;

Crossrefs

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

Sequence in context: A144207 A016487 A370707 * A374282 A260430 A243347

Adjacent sequences: A104060 A104061 A104062 * A104064 A104065 A104066

Keyword

sign,tabf

Author

Emeric Deutsch, Mar 02 2005

Status

approved