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A331757 Number of edges in a figure made up of a row of n adjacent congruent rectangles upon drawing diagonals of all possible rectangles. 13
8, 28, 80, 178, 372, 654, 1124, 1782, 2724, 3914, 5580, 7626, 10352, 13590, 17540, 22210, 28040, 34670, 42760, 51962, 62612, 74494, 88508, 104042, 121912, 141534, 163664, 187942, 215636, 245490, 279260, 316022, 356456, 399898, 447612, 498698, 555352 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..37.

Lars Blomberg, Scott R. Shannon, N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2020). Also arXiv:2009.07918.

FORMULA

a(n) = 2*n + 2 + 3*A324042(n) + 4*A324043(n).

MATHEMATICA

Table[n^2 + 4n + 1 + Sum[Sum[(2 * Boole[GCD[i, j] == 1] - Boole[GCD[i, j] == 2]) * (n + 1 - i) * (n + 1 - j), {j, 1, n}], {i, 1, n}], {n, 1, 37}] (* Joshua Oliver, Feb 05 2020 *)

CROSSREFS

A306302 gives number of regions in the figure.

This is column 1 of A331454.

Cf. A324042, A324043.

Sequence in context: A134638 A293289 A305638 * A130129 A317032 A229713

Adjacent sequences:  A331754 A331755 A331756 * A331758 A331759 A331760

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 04 2020

STATUS

approved

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)