A048773 Partial sums of A048697.

1, 11, 32, 84, 209, 511, 1240, 3000, 7249, 17507, 42272, 102060, 246401, 594871, 1436152, 3467184, 8370529, 20208251, 48787040, 117782340, 284351729, 686485807, 1657323352, 4001132520, 9659588401, 23320309331, 56300207072, 135920723484, 328141654049

Offset: 0

Author

Barry E. Williams

Keywords

• easy
• nice
• nonn

Links

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

Crossrefs

Cf. A001333, A000129, A048696, A048697.

Programs

Mathematica

Accumulate[LinearRecurrence[{2,1},{1,10},35]] (* Harvey P. Dale, Jul 26 2011 *)
LinearRecurrence[{3, -1, -1},{1, 11, 32},29] (* Ray Chandler, Aug 03 2015 *)

Formula

a(n) = 2*a(n-1)+a(n-2)+9; a(0)=1, a(1)=11.

a(n) = (((10+(11/2)*sqrt(2))*(1+sqrt(2))^n - (10-(11/2)*sqrt(2))*(1-sqrt(2))^n)/ 2*sqrt(2))-9/2.

From R. J. Mathar, Nov 08 2012: (Start)

G.f.: ( 1+8*x ) / ( (x-1)*(x^2+2*x-1) ).

a(n) = A048739(n)+8*A048739(n-1). (End)

a(n) = 3*a(n-1)-a(n-2)-a(n-3). - Wesley Ivan Hurt, May 21 2021

Extensions

More terms from Harvey P. Dale, Jul 26 2011