A339487 a(n) is the area of the n-gon with vertices (3^i, 5^i) for 0 <= i <= n-1.

8, 192, 3344, 52800, 806168, 12166272, 182871584, 2744987520, 41184460328, 617815378752, 9267473759024, 139013323899840, 2085205952447288, 31278119775589632, 469171949135641664, 7037579999715797760, 105563703809659391048, 1583455576216052670912, 23751833738601248135504, 356277506555834959529280

Offset

3,1

Links

Robert Israel, Table of n, a(n) for n = 3..851

Index entries for linear recurrences with constant coefficients, signature (24, -158, 360, -225).

Formula

a(n) = -1/14 - 5^n/10 + 3^n/6 + 15^n/210.

G.f.: 8*x^3/(225*x^4-360*x^3+158*x^2-24*x+1).

Example

a(3) is the area of the triangle with vertices (1,1), (3,5) and (9,25), which is 8.

Maple

f:= n -> -1/14 - 5^n/10 + 3^n/6 + 15^n/210:
map(f, [$3..30]);

Mathematica

Drop[CoefficientList[Series[8 x^3/(225 x^4 - 360 x^3 + 158 x^2 - 24 x + 1), {x, 0, 22}], x], 3] (* Michael De Vlieger, Dec 07 2020 *)

Crossrefs

Sequence in context: A275995 A129004 A267948 * A189537 A268095 A058873

Adjacent sequences: A339484 A339485 A339486 * A339488 A339489 A339490

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 07 2020

Status

approved