A121164 Triangle, real terms extracted from squares of paired terms in arithmetic sequences.

-3, -8, -5, -15, -16, -7, -24, -33, -24, -9, -35, -56, -51, -32, -11, -48, -85, -88, -69, -40, -13, -63, -120, -135, -120, -87, -48, -15, -80, -161, -192, -185, -152, -105, -56, -17, -99, -208, -259, -264, -235, -184, -123, -19, -120, -261, -336, -357, -336, -285, -216, -141

Offset

1,1

Comments

Left border (-3, -8, -15, -24, ...) unsigned = A013648. Next column (-5, -16, -33, ...) unsigned = A045944.

Links

Table of n, a(n) for n=1..52.

Formula

Form an array of the arithmetic sequences: (1, 2, 3, ...); (1, 3, 5, ...); (1, 4, 7, ...); and consider each pair as a complex term; e.g., (1 + 2i), (2 + 3i), then square each complex term and extract the real integer. Antidiagonals become rows of the triangle.

Example

Array of the extracted real terms:
   -3,  -5,  -7,   -9, ...
   -8, -16, -24,  -32, ...
  -15, -33, -51,  -69, ...
  -24, -56, -88, -120, ...
  ...
Taking antidiagonals we get the triangle:
   -3;
   -8,  -5;
  -15, -16,  -7;
  -24, -33, -24,  -9;
  -35, -56, -51, -32, -11;
  -48, -85, -88, -69, -40, -13;
  ...
(3,2) = -16 since (taken from the arithmetic sequence 1, 3, 5, ...), (3 + 5i)^2 = (-16 + 30i).

Crossrefs

Cf. A013648, A045944.

Sequence in context: A166492 A120070 A143753 * A086872 A363421 A323760

Adjacent sequences: A121161 A121162 A121163 * A121165 A121166 A121167

Keyword

sign,tabl

Author

Gary W. Adamson, Aug 13 2006

Status

approved