A296796 Numbers k such that k is the altitude of a Heronian triangle with sides m - 11, m, m + 11.
12, 15, 33, 63, 72, 132, 240, 273, 495, 897, 1020, 1848, 3348, 3807, 6897, 12495, 14208, 25740, 46632, 53025, 96063, 174033, 197892, 358512, 649500, 738543, 1337985, 2423967, 2756280, 4993428, 9046368, 10286577, 18635727, 33761505, 38390028, 69549480
Offset: 0
Examples
If the sides are 17, 28, 39 the triangle has the altitude 15 against 28 and is a part of the Pythagorean triangle with the sides 15, 36, 39, so 15 is a term.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,0,4,0,0,-1).
Programs
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Mathematica
CoefficientList[Series[3 (4 + 5 x + 11 x^2 + 5 x^3 + 4 x^4)/(1 - 4 x^3 + x^6), {x, 0, 35}], x] (* Michael De Vlieger, Dec 22 2017 *) -
PARI
Vec(3*(4 + 5*x + 11*x^2 + 5*x^3 + 4*x^4) / (1 - 4*x^3 + x^6) + O(x^40)) \\ Colin Barker, Dec 22 2017
Formula
From Colin Barker, Dec 22 2017: (Start)
G.f.: 3*(4 + 5*x + 11*x^2 + 5*x^3 + 4*x^4) / (1 - 4*x^3 + x^6).
a(n) = 4*a(n-3) - a(n-6) for n>5.
(End)
Extensions
More terms from Colin Barker, Dec 22 2017
Comments