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 A374011 a(n) = (1 + (n+9)^2 - (n-10)*(-1)^n)/2. 9
 46, 65, 69, 88, 96, 115, 127, 146, 162, 181, 201, 220, 244, 263, 291, 310, 342, 361, 397, 416, 456, 475, 519, 538, 586, 605, 657, 676, 732, 751, 811, 830, 894, 913, 981, 1000, 1072, 1091, 1167, 1186, 1266, 1285, 1369, 1388, 1476, 1495, 1587, 1606, 1702, 1721, 1821 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 10 of the boustrophedon-style array (see example). In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=10. LINKS Table of n, a(n) for n=1..51. Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). G.f.: -x*(46*x^4-19*x^3-88*x^2+19*x+46)/((x+1)^2*(x-1)^3). a(n) = A374010(n+1) + (-1)^n. EXAMPLE [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12] [ 1] 1 3 4 10 11 21 22 36 37 55 56 78 ... [ 2] 2 5 9 12 20 23 35 38 54 57 77 ... [ 3] 6 8 13 19 24 34 39 53 58 76 ... [ 4] 7 14 18 25 33 40 52 59 75 ... [ 5] 15 17 26 32 41 51 60 74 ... [ 6] 16 27 31 42 50 61 73 ... [ 7] 28 30 43 49 62 72 ... [ 8] 29 44 48 63 71 ... [ 9] 45 47 64 70 ... [10] 46 65 69 ... [11] 66 68 ... [12] 67 ... ... MATHEMATICA CoefficientList[Series[-(46*x^4 - 19*x^3 - 88*x^2 + 19*x + 46)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x] k := 10; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}] PROG (Magma) [(1 + (n+9)^2 - (n-10)*(-1)^n)/2: n in [1..80]]; CROSSREFS For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), A374007 (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), this sequence (k=10). Row 10 of the table in A056011. Column 10 of the rectangular array in A056023. Sequence in context: A043247 A044027 A020175 * A118698 A350203 A103381 Adjacent sequences: A374008 A374009 A374010 * A374012 A374013 A374014 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Jun 24 2024 STATUS approved

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Last modified September 16 02:10 EDT 2024. Contains 375959 sequences. (Running on oeis4.)