A337640 a(n) = one-half of the number of cells in the central rectangle of the graph described in row 2n+1 of A333288.

2, 11, 35, 80, 155, 266, 422, 626, 890, 1223, 1625, 2108, 2678, 3341, 4109, 4988, 5990, 7106, 8348, 9734, 11264, 12953, 14801, 16820, 19019, 21389, 23957, 26717, 29663, 32834, 36230, 39860, 43712, 47795, 52139, 56726, 61598, 66746, 72152, 77837

Offset: 0

Author

N. J. A. Sloane, Sep 17 2020

Keywords

• nonn

Comments

This is based on Lars Blomberg's data in A333288.

A333288 is a triangular array read by rows. a(n) is the central term in row 2n+1 of that triangle, divided by 2.

See A331452 for further illustrations.

It would be nice to have a formula for this sequence. It is possible that focusing on the points (n, a(n)) where 2n+1 is a prime might lead to a simpler formula.

Links

• Scott R. Shannon, Colored illustration for a(0): there are 4 regions, so a(0) = 2.
• Scott R. Shannon, Colored illustration for a(1): the central square has 22 regions, so a(1) = 11.
• Scott R. Shannon, Colored illustration for a(2): the central square has 70 regions, so a(2) = 35.
• Scott R. Shannon, Colored illustration for a(3): the central square has 160 regions, so a(3) = 80.
• Scott R. Shannon, Colored illustration for a(4): the central square has 310 regions, so a(4) = 155.

Crossrefs

Cf. A306302, A331452, A333288.