A116454 Smallest m such that A116452(m) = n.

0, 2, 9, 25, 59, 129, 271, 557, 1131, 2281, 4583, 9189, 18403, 36833, 73695, 147421, 294875, 589785, 1179607, 2359253, 4718547, 9437137, 18874319, 37748685, 75497419, 150994889, 301989831, 603979717, 1207959491, 2415919041

Offset: 1

Author

Reinhard Zumkeller, Feb 16 2006

Keywords

• nonn

Comments

A116451(a(n)) = A116453(n);

Primes include a(2) = 2, a(5) = 59, a(7) = 271, a(8) = 557, a(10) = 2281, a(11) = 4583, a(14) = 36833. - Jonathan Vos Post, Feb 20 2006

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -5, 2).

Programs

Mathematica

Join[{0},RecurrenceTable[{a[1]==2,a[n]==2(a[n-1]+n)+1},a[n],{n,30}]] (* or *) Join[{0},LinearRecurrence[{4,-5,2},{2,9,25},30]] (* Harvey P. Dale, Jul 18 2011 *)

Formula

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

a(0)=0, a(1)=2, a(2)=9, a(3)=25, a(n)=4*a(n-1)-5*a(n-2)+2*a(n-3) [From Harvey P. Dale, Jul 18 2011]

G.f.: ((x-2)*x*(x+1))/((x-1)^2*(2*x-1)) [From Harvey P. Dale, Jul 18 2011]