A164560 Partial sums of A164532.

1, 5, 11, 35, 71, 215, 431, 1295, 2591, 7775, 15551, 46655, 93311, 279935, 559871, 1679615, 3359231, 10077695, 20155391, 60466175, 120932351, 362797055, 725594111, 2176782335, 4353564671, 13060694015, 26121388031, 78364164095

Offset: 1

Author

Klaus Brockhaus, Aug 16 2009

Keywords

• nonn
• easy

Comments

Interleaving of A164559 and A024062 without initial term 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..900
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6).

Crossrefs

Cf. A164532, A164123 (partial sums of A162436), A164559 (6^n/3-1), A024062 (6^n-1), A026549.

Programs

Magma

T:=[ n le 2 select 3*n-2 else 6*Self(n-2): n in [1..28] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T]];

Formula

a(n) = 6*a(n-2)+5 for n > 2; a(1) = 1, a(2) = 5.

a(n) = (3-(-1)^n)*6^(1/4*(2*n-1+(-1)^n))/2-1.

G.f.: x*(1+4*x)/((1-x)*(1-6*x^2)).

a(n) = A026549(n) - 1.