OFFSET
0,2
COMMENTS
Using the data that is available from Lars Blomberg, and the nine possible arrangements, (a), of the three sides, here are those counts for the first x terms not including a(0):
\x. 10 100 1000 10000 100000 1000000 3000000 aprx percentage.
a\
11:. 3. 21. 164. 1502. 13734. 134087. 401166 ~13.3%
12:. 1. 18. 215. 2120. 21457. 208304. 621859 ~20.7%
13:. 0.. 6.. 94.. 921.. 8884.. 86286. 256802. ~8.5%
21:. 0.. 3.. 51.. 550.. 5120.. 51732. 156588. ~5.2%
22:. 3. 22. 207. 2025. 21013. 214855. 646185 ~21.6%
23:. 0.. 5.. 55.. 657.. 6347.. 64480. 194775. ~6.5%
31:. 2. 12.. 95.. 881.. 8697.. 83631. 249413. ~8.3%
32:. 1.. 7.. 51.. 390.. 4219.. 42112. 126410. ~4.2%
33:. 0.. 6.. 68.. 954. 10529. 114513. 346802 ~11.7%
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..10000
EXAMPLE
a(2)=31 because 5 is the hypotenuse in the 3-4-5 Pythagorean triple, a(n-1) is 4 and 5 is the lesser side in the 5-12-13 Pythagorean triple, a(n+1) is 12.
MATHEMATICA
lst={ (* the terms from A235598 *) }; g[j_, k_] := Block[{hyp = Sqrt[ j^2 + k^2], lg = Abs@ Sqrt[ j^2 - k^2]}, If[ IntegerQ@ hyp, If[ Min[j, k] == k, 1, 2], If[ Max[j, k] == k, 3, If[lg > k, 1, 2]]]]; f[n_] := Block[{s = Take[lst, {n - 1, n + 1}]}, 10g[ s[[1]], s[[2]] ] + g[ s[[3]], s[[2]] ]]; f[1] = 1; Array[f, 80]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 20 2014
STATUS
approved