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%I #33 May 25 2024 15:35:00
%S 2,9,4,18,6,27,8,36,10,45,12,54,14,63,16,72,18,81,20,90,22,99,24,108,
%T 26,117,28,126,30,135,32,144,34,153,36,162,38,171,40,180,42,189,44,
%U 198,46,207,48,216,50,225,52,234,54,243,56,252,58,261,60,270,62,279,64,288
%N Table read by rows; T(n,k) = 2n for k = 1, T(n,k) = 9n for k = 2.
%C The members of each pair [T(n,1),T(n,2)] create the same sequence of curvatures (rounded down) of circles after offset of the first 4 terms. See the pattern construction rule and formulas in links. Let the legs' length a = b = T(n,k). See also illustration in links; T(1,1) and T(1,2) create the same sequence, but it is different from the one created by both T(2,1), and T(2,2). Are they have repeated sequences between pairs?
%C Positive terms of A005843 and positive terms of A008591 interleaved. - _Omar E. Pol_, Sep 14 2013
%H Kival Ngaokrajang, <a href="/A228967/a228967.pdf">Illustration for [T(1,1),T(1,2)] and [T(2,1),T(2,2)]</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RightTriangle.html">Right Triangle</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F a(n) = 2a(n-2) - a(n-4). - _Charles R Greathouse IV_, Sep 10 2013
%e Table begins:
%e n/k 1 2
%e 1 2 9
%e 2 4 18
%e 3 6 27
%e 4 8 36
%e ...
%t LinearRecurrence[{0,2,0,-1},{2,9,4,18},80] (* _Harvey P. Dale_, Sep 21 2019 *)
%o (PARI) vector(80,n,(n+1)\2*if(n%2,2,9)) \\ _Charles R Greathouse IV_, Sep 10 2013
%K nonn,easy,tabf
%O 1,1
%A _Kival Ngaokrajang_, Sep 10 2013
%E Corrected by _Charles R Greathouse IV_, Sep 10 2013