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A374009
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a(n) = (1 + (n+7)^2 - (n-8)*(-1)^n)/2.
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9
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29, 44, 48, 63, 71, 86, 98, 113, 129, 144, 164, 179, 203, 218, 246, 261, 293, 308, 344, 359, 399, 414, 458, 473, 521, 536, 588, 603, 659, 674, 734, 749, 813, 828, 896, 911, 983, 998, 1074, 1089, 1169, 1184, 1268, 1283, 1371, 1386, 1478, 1493, 1589, 1604, 1704, 1719
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OFFSET
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1,1
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COMMENTS
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Fill an array with the natural numbers n = 1,2,... along diagonals in alternating 'down' and 'up' directions. a(n) is row 8 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=8.
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LINKS
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FORMULA
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a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: -x*(29*x^4-15*x^3-54*x^2+15*x+29)/((x+1)^2*(x-1)^3).
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EXAMPLE
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[ 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 ...
...
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MATHEMATICA
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CoefficientList[Series[-(29*x^4 - 15*x^3 - 54*x^2 + 15*x + 29)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 8; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]
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PROG
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(Magma) [(1 + (n+7)^2 - (n-8)*(-1)^n)/2: n in [1..80]];
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CROSSREFS
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Column 8 of the rectangular array in A056023.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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