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

0,2

Links

Table of n, a(n) for n=0..26.

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

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

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 *)

Crossrefs

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

Sequence in context: A358246 A048467 A002765 * A055273 A296323 A241353

Adjacent sequences: A048767 A048768 A048769 * A048771 A048772 A048773

Keyword

nonn,easy,nice

Author

Barry E. Williams

Extensions

More terms from James A. Sellers, Jun 20 2000

Status

approved