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URL: https://oeis.org/A382608

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A382608
Long leg of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
5
0, 4, 4, 12, 24, 60, 144, 364, 924, 2380, 6160, 16020, 41760, 109044, 285012, 745420, 1950312, 5104012, 13359280, 34969884, 91543980, 239651724, 627394464, 1642504612, 4300075584, 11257651300, 29472763684, 77160454284, 202008299064, 528863957340, 1384582787280
OFFSET
0,2
LINKS
FORMULA
a(n) = 2*F(n)*(F(n) + 1) where F(n) = A000045(n).
From Andrew Howroyd, Nov 13 2025: (Start)
a(n) = 4*A033192(n).
G.f.: 4*x*(1 - 2*x - x^2 + x^3)/((1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). (End)
EXAMPLE
Triangle begins:
n=1: 3, 4, 5;
n=2: 3, 4, 5;
n=3: 5, 12, 13;
where this sequence is the middle column.
MATHEMATICA
a=Table[Fibonacci[n], {n, 0, 16}]; Apply[Join, Map[{2#+1, 2#^2+2#, 2#^2+2#+1}&, a]]
PROG
(PARI) a(n) = 2*fibonacci(n)*(fibonacci(n) + 1); \\ Andrew Howroyd, Nov 13 2025
CROSSREFS
Cf. A000045 (inradius), A001588 (short leg), A382609 (semiperimeter), A382610 (area), A033192.
Sequence in context: A303644 A298796 A106232 * A359709 A228612 A038804
KEYWORD
nonn,easy
EXTENSIONS
a(0)=0 prepended by Andrew Howroyd, Nov 13 2025
STATUS
approved