A358408 -id:A358408 - cp's OEIS frontend

A358407 Number of regions formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.

1, 5, 37, 173, 553, 1365, 2909, 5513, 9577, 15485, 24157, 35021, 51201, 71013, 95621, 126277, 167213, 211737, 272025, 335681, 413677, 505445, 618557, 729485, 878017, 1034697, 1215185, 1409273, 1654785, 1875265, 2192281, 2486797, 2836317, 3216833, 3633709, 4034313, 4599789, 5124841

Offset: 1

Scott R. Shannon, Nov 14 2022

nonn

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 = 10.
Scott R. Shannon, Image for n = 20.

Cf. A358408 (vertices), A358409 (edges), A355798, A255011.

a(n) = A358409(n) - A358408(n) + 1 by Euler's formula.

A358409 Number of edges formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.

Original entry on oeis.org

4, 12, 68, 316, 1020, 2524, 5420, 10348, 18044, 29244, 45940, 66188, 97796, 135772, 182532, 240932, 321612, 405852, 525184, 646088, 796388, 974740, 1199244, 1407140, 1700944, 2004576, 2356296, 2729256, 3221296, 3630296, 4272656, 4835984, 5522768, 6269016, 7084056, 7835068, 8987192, 10005400

Offset: 1

Scott R. Shannon, Nov 14 2022

nonn

See A358407 and A358408 for images of the square.

Cf. A358407 (regions), A358408 (vertices), A355800, A331448.

a(n) = A358407(n) + A358408(n) - 1 by Euler's formula.

cp's OEIS Frontend

A358407 Number of regions formed in a square by straight line segments when connecting the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on each of the two adjacent edges of the square.

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