

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
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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



