A331449 a(0) = 1 by convention; for n>0, a(n) is the number of points in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).

1, 5, 37, 257, 817, 2757, 4825, 12293, 19241, 33549, 49577, 87685, 101981, 178465, 220113, 286357, 379097, 551669, 606241, 880293, 951445, 1209049, 1507521, 1947877, 2002669, 2624409, 3056093, 3550425, 3955049, 5069037, 5062153, 6669665, 7081969, 8143193, 9365089, 10296469

Offset

0,2

Comments

Equivalently, this is A334690(n) + 4*n.

Links

Lars Blomberg, Table of n, a(n) for n = 0..52

Lars Blomberg, Scott R. Shannon, and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2021). Also arXiv:2009.07918.

N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 20.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 10.

Formula

By Euler's formula, a(n) = A331448(n) - A255011(n) + 1.

Crossrefs

Cf. A255011, A331448.

For the circular analog see A006533, A007678, A007569, A135565.

Sequence in context: A080507 A108049 A121141 * A220634 A083232 A236581

Adjacent sequences: A331446 A331447 A331448 * A331450 A331451 A331452

Keyword

nonn

Author

N. J. A. Sloane, Jan 23 2020

Extensions

a(11)-a(35) from Giovanni Resta, Jan 28 2020

Status

approved