cp's OEIS Frontend

A374007 a(n) = (1 + (n+5)^2 - (n-6)*(-1)^n)/2.

%I A374007 #7 Jun 24 2024 19:24:53
%S A374007 16,27,31,42,50,61,73,84,100,111,131,142,166,177,205,216,248,259,295,
%T A374007 306,346,357,401,412,460,471,523,534,590,601,661,672,736,747,815,826,
%U A374007 898,909,985,996,1076,1087,1171,1182,1270,1281,1373,1384,1480,1491,1591,1602
%N A374007 a(n) = (1 + (n+5)^2 - (n-6)*(-1)^n)/2.
%C A374007 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).
%C A374007 In general, row k is given by (1+t^2+(n-k)*(-1)^t)/2, t = n+k-1. Here, k=6.
%H A374007 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A374007 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F A374007 G.f.: -x*(16*x^4-11*x^3-28*x^2+11*x+16)/((x+1)^2*(x-1)^3).
%F A374007 a(n) = A374005(n+1) + (-1)^n.
%e A374007        [ 1] [ 2] [ 3] [ 4] [ 5] [ 6] [ 7] [ 8] [ 9] [10] [11] [12]
%e A374007   [ 1]   1    3    4   10   11   21   22   36   37   55   56   78   ...
%e A374007   [ 2]   2    5    9   12   20   23   35   38   54   57   77   ...
%e A374007   [ 3]   6    8   13   19   24   34   39   53   58   76   ...
%e A374007   [ 4]   7   14   18   25   33   40   52   59   75   ...
%e A374007   [ 5]  15   17   26   32   41   51   60   74   ...
%e A374007   [ 6]  16   27   31   42   50   61   73   ...
%e A374007   [ 7]  28   30   43   49   62   72   ...
%e A374007   [ 8]  29   44   48   63   71   ...
%e A374007   [ 9]  45   47   64   70   ...
%e A374007   [10]  46   65   69   ...
%e A374007   [11]  66   68   ...
%e A374007   [12]  67   ...
%e A374007         ...
%t A374007 CoefficientList[Series[-(16*x^4 - 11*x^3 - 28*x^2 + 11*x + 16)/((x + 1)^2*(x - 1)^3), {x, 0, 50}], x]
%t A374007 k := 6; Table[(1 + (n + k - 1)^2 + (n - k) (-1)^(n + k - 1))/2, {n, 80}]
%o A374007 (Magma) [(1 + (n+5)^2 - (n-6)*(-1)^n)/2: n in [1..80]];
%Y A374007 For rows k = 1..10: A131179 (k=1) n>0, A373662 (k=2), A373663 (k=3), A374004 (k=4), A374005 (k=5), this sequence (k=6), A374008 (k=7), A374009 (k=8), A374010 (k=9), A374011 (k=10).
%Y A374007 Row 6 of the table in A056011.
%Y A374007 Column 6 of the rectangular array in A056023.
%K A374007 nonn,easy
%O A374007 1,1
%A A374007 _Wesley Ivan Hurt_, Jun 24 2024