A164053 Partial sums of A162255.

3, 5, 11, 15, 27, 35, 59, 75, 123, 155, 251, 315, 507, 635, 1019, 1275, 2043, 2555, 4091, 5115, 8187, 10235, 16379, 20475, 32763, 40955, 65531, 81915, 131067, 163835, 262139, 327675, 524283, 655355, 1048571, 1310715, 2097147, 2621435, 4194299

Offset: 1

Author

Klaus Brockhaus, Aug 08 2009

Keywords

• nonn

Comments

Apparently a(n) = A094958(n+4)-5.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 2, -2).

Crossrefs

Cf. A162255, A094958.

Programs

Magma

T:=[ n le 2 select 4-n else 2*Self(n-2): n in [1..39] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T]];

Mathematica

Accumulate[LinearRecurrence[{0,2},{3,2},50]] (* or *) LinearRecurrence[ {1,2,-2},{3,5,11},50] (* Harvey P. Dale, Aug 28 2012 *)

PARI

x='x+O('x^50); Vec(x*(3+2*x)/(1-x-2*x^2+2*x^3)) \\ G. C. Greubel, Sep 09 2017

Formula

a(n) = 2*a(n-2) + 5 for n > 2; a(1) = 3, a(2) = 5.

a(n) = (13 - 3*(-1)^n)*2^(1/4*(2*n -1 +(-1)^n))/2 - 5.

G.f.: x*(3+2*x)/(1-x-2*x^2+2*x^3).

a(1)=3, a(2)=5, a(3)=11, a(n)=a(n-1)+2*a(n-2)-2*a(n-3). - Harvey P. Dale, Aug 28 2012