

A355902


Start with a 2 X n array of squares, join every vertex on top edge to every vertex on bottom edge; a(n) = onehalf the number of cells.


2



0, 3, 10, 26, 56, 112, 196, 331, 522, 790, 1138, 1615, 2204, 2975, 3910, 5041, 6388, 8047, 9958, 12262, 14894, 17920, 21346, 25347, 29796, 34875, 40522, 46854, 53826, 61716, 70274, 79883, 90380, 101875, 114346, 127981, 142612, 158737, 176086, 194827, 214852, 236717, 259906, 285124, 311970, 340588, 370990, 403819, 438440, 475556
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OFFSET

0,2


COMMENTS

Note that this figure can be obtained by drawing an "equatorial" line through the middle of the strip of n adjacent rectangles in A306302. This cuts each of the 2n "equatorial" cells in A306302 in two. It follows that 2*a(n) = A306302(n) + 2*n, i.e. that a(n) = A306302(n)/2 + n. Note that there is an explicit formula for A306302(n) in terms of n.  Scott R. Shannon, Sep 06 2022.
This means the present sequence is one more member of the large class of sequences which are essentially the same as A115004 (see CrossReferences).  N. J. A. Sloane, Sep 06 2022


LINKS

Scott R. Shannon, Image for a(4) = 56. Note in this and other images the entire 2xn array is shown so the number of cells is twice a(n).


FORMULA



CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



