A218220 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.

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, 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, 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

Offset

0,18

Comments

Variant of A094954 and A162997.

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

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

a(n,2)=1

a(n,3) is alternating Fibonacci numbers.

Links

Table of n, a(n) for n=0..100.

Example

   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,...
   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,...
  -1,   0,   1,   2,   3,   4,   5,   6,   7,   8,   9,...
  -1,  -1,   1,   5,  11,  19,  29,  41,  55,  71,  89,...
   1,  -1,   1,  13,  41,  91, 169, 281, 433, 631, 881,...
   1,   0,   1,  34, 153, 436, 985,1926,3409,5608,8721,...
  -1,   1,   1,  89, 571,2089,5741,13201,26839,49841,86329,...
  -1,   1,   1, 233,2131,10009,33461,90481,211303,442961,854569,...

Crossrefs

Cf. A218219.

Sequence in context: A193518 A060176 A305297 * A247487 A010248 A325403

Adjacent sequences: A218217 A218218 A218219 * A218221 A218222 A218223

Keyword

sign,tabl,easy,changed

Author

Nico Brown, Oct 23 2012

Status

approved