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 6 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=6.
LINKS
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*(16*x^4-11*x^3-28*x^2+11*x+16)/((x+1)^2*(x-1)^3).
a(n) = A374005(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[-(16*x^4 - 11*x^3 - 28*x^2 + 11*x + 16)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
k := 6; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]
PROG
(Magma) [(1 + (n+5)^2 - (n-6)*(-1)^n)/2: n in [1..80]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 24 2024
STATUS
approved