%I #10 Apr 27 2024 17:22:02

%S 1,1,1,1,1,-1,1,1,0,-1,1,1,1,-1,1,1,1,2,1,-1,1,1,1,3,5,1,0,-1,1,1,4,

%T 11,13,1,1,-1,1,1,5,19,41,34,1,1,1,1,1,6,29,91,153,89,1,0,1,1,1,7,41,

%U 169,436,571,233,1,-1,-1,1,1,8,55,281,985,2089,2131,610,1,-1,-1,1,1,9,71,433,1926,5741,10009,7953,1597,1,0,1,1,1,10,89,631,3409,13201,33461,47956,29681

%N Array a(n,m) read by antidiagonals where a(0,m)=a(1,m)=1 and a(n,m) = m*a(n-1,m)-a(n-2,m) for n>=2.

%C Variant of A094954 and A162997.

%C a(n,0) alternates 1,1,-1,-1,1,1,...

%C a(n,1) alternates 1,1,0,-1,-1,0,...

%C a(n,2)=1

%C a(n,3) is alternating Fibonacci numbers.

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...

%e -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...

%e -1, -1, 1, 5, 11, 19, 29, 41, 55, 71, 89,...

%e 1, -1, 1, 13, 41, 91, 169, 281, 433, 631, 881,...

%e 1, 0, 1, 34, 153, 436, 985,1926,3409,5608,8721,...

%e -1, 1, 1, 89, 571,2089,5741,13201,26839,49841,86329,...

%e -1, 1, 1, 233,2131,10009,33461,90481,211303,442961,854569,...

%Y Cf. A218219.

%K sign,tabl,easy

%O 0,18

%A _Nico Brown_, Oct 23 2012