A048755 Partial sums of A048693.

1, 7, 20, 52, 129, 315, 764, 1848, 4465, 10783, 26036, 62860, 151761, 366387, 884540, 2135472, 5155489, 12446455, 30048404, 72543268, 175134945, 422813163, 1020761276, 2464335720, 5949432721, 14363201167, 34675835060, 83714871292, 202105577649, 487926026595

Offset

0,2

Links

Table of n, a(n) for n=0..29.

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

Formula

a(n)=2*a(n-1)+a(n-2)+5; a(0)=1, a(1)=6.

a(n)=[ {(6+(7/2)*sqrt(2))(1+sqrt(2))^n - (6-(7/2)*sqrt(2))(1-sqrt(2))^n}/ 2*sqrt(2) ]-5/2.

G.f. ( 1+4*x ) / ( (x-1)*(x^2+2*x-1) ). - R. J. Mathar, Nov 08 2012

a(0)=1, a(1)=7, a(2)=20, a(n)=3*a(n-1)-a(n-2)-a(n-3). - Harvey P. Dale, Mar 29 2013

Mathematica

Accumulate[LinearRecurrence[{2, 1}, {1, 6}, 30]] (* or *) LinearRecurrence[ {3, -1, -1}, {1, 7, 20}, 40] (* Harvey P. Dale, Mar 29 2013 *)

Crossrefs

Cf. A048693, A048654, A048655.

Sequence in context: A047862 A264879 A320681 * A055267 A218843 A219422

Adjacent sequences: A048752 A048753 A048754 * A048756 A048757 A048758

Keyword

easy,nonn

Author

Barry E. Williams

Extensions

More terms from Harvey P. Dale, Mar 29 2013

Status

approved