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A145009 Triangle read by rows: array of odd integers found in |A144912| with axes b = {4, 6, 8, ...} and n = {b^2, b^4, b^6, ...}. 0
7, 13, 13, 19, 23, 19, 25, 33, 33, 25, 31, 43, 47, 43, 31, 37, 53, 61, 61, 53, 37, 43, 63, 75, 79, 75, 63, 43, 49, 73, 89, 97, 97, 89, 73, 49, 55, 83, 103, 115, 119, 115, 103, 83, 55, 61, 93, 117, 133, 141, 141, 133, 117, 93, 61 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The complete array can be defined as 6(x + y) + 4xy + 7.

Values along the edges are given by 6x + 7 and thus include the larger member of every twin prime pair except 5. The smaller member, 6x + 5, is adjacent in |A144912|.

Taking the origin to be z = 1, the main diagonal is given by 4z^2 + 4z - 1 (A073577).

Sums along antidiagonals are given by z(2z^2 + 12z + 7) / 3.

Contribution from Reikku Kulon, Sep 29 2008: (Start)

Any entry in the triangle can be produced from the two terms diagonally above or below and the edges can be found by taking the odd numbers as the "missing" values, starting from 1. If the terms are denoted:

.. a0 .. ...

a1 .. a2 ...

.. a3 .. ...

then:

a0 = (a1 + a2 + 4) / 2 - sqrt(a1^2 + 8 * a1 - 2 * a1 * a2 + 8 * a2 + a2^2 + 48) / 2;

a3 = (a1 + a2 + 4) / 2 + sqrt(a1^2 + 8 * a1 - 2 * a1 * a2 + 8 * a2 + a2^2 + 48) / 2. (End)

LINKS

Table of n, a(n) for n=0..54.

CROSSREFS

Cf. A000040, A006512, A073577, A144912

Sequence in context: A135555 A243044 A229831 * A090229 A259222 A204713

Adjacent sequences:  A145006 A145007 A145008 * A145010 A145011 A145012

KEYWORD

easy,nonn,tabl

AUTHOR

Reikku Kulon, Sep 28 2008

STATUS

approved

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Last modified May 28 10:46 EDT 2017. Contains 287240 sequences.