cp's OEIS Frontend

Similar sequences, where P(s, m) = ((s-2)*m^2-(s-4)*m)/2 is the m-th s-gonal number:

A000578: P(3, m)*P( 3, m) - P(3, m-1)*P( 3, m-1);

A213772: P(3, m)*P( 4, m) - P(3, m-1)*P( 4, m-1) for m>0;

A005915: P(3, m)*P( 5, m) - P(3, m-1)*P( 5, m-1) " ;

A130748: P(3, m)*P( 6, m) - P(3, m-1)*P( 6, m-1) for m>1;

A027849: P(3, m)*P( 7, m) - P(3, m-1)*P( 7, m-1) for m>0;

A214092: P(3, m)*P( 8, m) - P(3, m-1)*P( 8, m-1) " ;

A100162: P(3, m)*P( 9, m) - P(3, m-1)*P( 9, m-1) " ;

A260260: P(3, m)*P(10, m) - P(3, m-1)*P(10, m-1), this sequence;

A100165: P(3, m)*P(11, m) - P(3, m-1)*P(11, m-1) for m>0.

The sequence is defined inductively as:

(a) it contains 0 and 4,

and

(b) for any nonzero term a(n), (2*a(n)) + 1 and 8*a(n) are also included as terms.

Because the inductive definition guarantees that all terms after 0 are of the form 7k+2, 7k+4 or 7k+5 (A047378), and because for any n >= 0, n^3 == 0, 1 or 6 (mod 7), (i.e., cubes are in A047275), it follows that there are no cubes in this sequence after the initial 0.