OFFSET
1,1
COMMENTS
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?
LINKS
Kival Ngaokrajang, Illustration for [T(1,1),T(1,2)] and [T(2,1),T(2,2)].
Eric Weisstein's World of Mathematics, Right Triangle.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(n) = 2a(n-2) - a(n-4). - Charles R Greathouse IV, Sep 10 2013
EXAMPLE
Table begins:
n/k 1 2
1 2 9
2 4 18
3 6 27
4 8 36
...
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {2, 9, 4, 18}, 80] (* Harvey P. Dale, Sep 21 2019 *)
PROG
(PARI) vector(80, n, (n+1)\2*if(n%2, 2, 9)) \\ Charles R Greathouse IV, Sep 10 2013
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Kival Ngaokrajang, Sep 10 2013
EXTENSIONS
Corrected by Charles R Greathouse IV, Sep 10 2013
STATUS
approved