A048770 Partial sums of A048694.

1, 8, 23, 60, 149, 364, 883, 2136, 5161, 12464, 30095, 72660, 175421, 423508, 1022443, 2468400, 5959249, 14386904, 34733063, 83853036, 202439141, 488731324, 1179901795, 2848534920, 6876971641, 16602478208, 40081928063

Offset: 0

Author

Barry E. Williams

Keywords

• nonn
• easy
• nice

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).

Crossrefs

Cf. A001333, A000129, A048654, A048655, A048694.

Programs

Mathematica

Accumulate[LinearRecurrence[{2,1},{1,7},40]] (* Harvey P. Dale, Jul 22 2011 *)
LinearRecurrence[{3, -1, -1},{1, 8, 23},27] (* Ray Chandler, Aug 03 2015 *)

Formula

a(n) = ((7+4*sqrt(2))*(1+sqrt(2))^n-(7-4*sqrt(2))*(1-sqrt(2))^n)/(2*sqrt(2))-3.

a(n) = 2*a(n-1)+a(n-2)+6 with n>1, a(0)=1, a(1)=8.

a(n) = 3*a(n-1)-a(n-2)-a(n-3). G.f.: (1+5*x)/((1-x)*(1-2*x-x^2)). - Colin Barker, Jun 23 2012

a(n) = 3*A000129(n)+4*A000129(n+1)-3. - R. J. Mathar, Sep 27 2012

Extensions

More terms from James Sellers, Jun 20 2000