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
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).
Programs
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Mathematica
Accumulate[LinearRecurrence[{2,1},{1,6},30]] (* or *) LinearRecurrence[ {3,-1,-1},{1,7,20},40] (* Harvey P. Dale, Mar 29 2013 *)
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
Extensions
More terms from Harvey P. Dale, Mar 29 2013