A292495 Triangle read by rows: T(n,k) = (-2)*T(n-1,k-1) + T(n,k-1) with T(2*m,0) = 0 and T(2*m+1,0) = (-1)^m.

0, 1, 1, 0, -2, -4, -1, -1, 3, 11, 0, 2, 4, -2, -24, 1, 1, -3, -11, -7, 41, 0, -2, -4, 2, 24, 38, -44, -1, -1, 3, 11, 7, -41, -117, -29, 0, 2, 4, -2, -24, -38, 44, 278, 336, 1, 1, -3, -11, -7, 41, 117, 29, -527, -1199, 0, -2, -4, 2, 24, 38, -44, -278, -336, 718

Offset

0,5

Links

Seiichi Manyama, Rows n = 0..139, flattened

Formula

T(n+1,n)^2 + T(n,n)^2 = 5^n.

Example

First few rows are:
   0;
   1,  1;
   0, -2, -4;
  -1, -1,  3,  11;
   0,  2,  4,  -2, -24;
   1,  1, -3, -11,  -7,  41;
   0, -2, -4,   2,  24,  38,  -44;
  -1, -1,  3,  11,   7, -41, -117, -29;
   0,  2,  4,  -2, -24, -38,   44, 278, 336.

Crossrefs

The diagonal of the triangle is related to A099456.

The next diagonal of the triangle is related to A139011.

Cf. A006495, A006496.

T(n,k) = b*T(n-1,k-1) + T(n,k-1): A292789 (b=-3), this sequence (b=-2), A117918 and A228405 (b=1), A227418 (b=2), A292466 (b=4).

Sequence in context: A362142 A139227 A269750 * A065626 A201758 A096110

Adjacent sequences: A292492 A292493 A292494 * A292496 A292497 A292498

Keyword

sign,tabl,look

Author

Seiichi Manyama, Sep 22 2017

Status

approved