A336630 a(n) = 2*F(2*n+1) + 4*F(n+1)*F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).

0, 4, 18, 38, 108, 274, 726, 1892, 4962, 12982, 33996, 88994, 232998, 609988, 1596978, 4180934, 10945836, 28656562, 75023862, 196415012, 514221186, 1346248534, 3524524428, 9227324738, 24157449798, 63245024644, 165577624146, 433487847782

Offset: 0

Author

Michael Tulskikh, Jul 28 2020

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,2,-1).

Crossrefs

Cf. A000045, A001519, A059929.

Formula

a(n) = (F(4n+1) - F(n+1)^4)/F(n)^2 for n > 0 and a(0) = 0, where F(n) = A000045(n).

a(n) = 2*A001519(n+1) + 4*A059929(n-1) for n > 0.

From Stefano Spezia, Jul 28 2020: (Start)

O.g.f.: 2*x*(2 + 5*x - 3*x^2)/(1 - 2*x - 2*x^2 + x^3).

a(n) = 2*a(n-1) + 2*a(n-2) - a(n-2) for n > 3. (End)