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 A355902 Start with a 2 X n array of squares, join every vertex on top edge to every vertex on bottom edge; a(n) = one-half 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 (list; graph; refs; listen; history; text; internal format)
 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 Cross-References). - N. J. A. Sloane, Sep 06 2022 LINKS Table of n, a(n) for n=0..49. 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). Scott R. Shannon, Image for a(6) = 196. Scott R. Shannon, Image for a(10) = 1138. Scott R. Shannon, Image for a(15) = 5041. N. J. A. Sloane, Illustration for a(2) = 10. N. J. A. Sloane, Illustration for a(3) = 26. FORMULA a(n) = A356790(2,n+2)/2 - 2. CROSSREFS Cf. A356790, A306302, A355798, A290131, A331452. The following nine sequences are all essentially the same. The simplest is A115004(n), which we denote by z(n). Then A088658(n) = 4*z(n-1); A114043(n) = 2*z(n-1)+2*n^2-2*n+1; A114146(n) = 2*A114043(n); A115005(n) = z(n-1)+n*(n-1); A141255(n) = 2*z(n-1)+2*n*(n-1); A290131(n) = z(n-1)+(n-1)^2; A306302(n) = z(n)+n^2+2*n; A355902(n) = n + A306302(n)/2. - N. J. A. Sloane, Sep 06 2022 Sequence in context: A343584 A335970 A212967 * A301410 A333897 A316937 Adjacent sequences: A355899 A355900 A355901 * A355903 A355904 A355905 KEYWORD nonn AUTHOR Scott R. Shannon and N. J. A. Sloane, Sep 05 2022 STATUS approved

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Last modified September 18 07:05 EDT 2024. Contains 375996 sequences. (Running on oeis4.)