A163979 a(n) = n*(n-1) + A144437(n+2).

1, 3, 5, 7, 15, 23, 31, 45, 59, 73, 93, 113, 133, 159, 185, 211, 243, 275, 307, 345, 383, 421, 465, 509, 553, 603, 653, 703, 759, 815, 871, 933, 995, 1057, 1125, 1193, 1261, 1335, 1409, 1483, 1563, 1643, 1723, 1809, 1895, 1981, 2073, 2165, 2257, 2355, 2453, 2551

Offset: 0

Author

Paul Curtz, Aug 07 2009

Keywords

• nonn
• easy

Comments

First differences are 2, 2, 2, 8, 8, 8, 14, 14, 14, 20, 20, 20,... (triplicated A016933).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Programs

Mathematica

LinearRecurrence[{2,-1,1,-2,1},{1,3,5,7,15},60]  (* or *) CoefficientList[ Series[-(1+x+5x^4-x^3)/((1+x+x^2)(x-1)^3), {x,0,60}],x]  (* Harvey P. Dale, Apr 20 2011 *)

PARI

x='x+O('x^50); Vec((1+x-x^3+5*x^4)/((1+x+x^2)*(1-x)^3)) \\ G. C. Greubel, Aug 24 2017

Formula

a(n) = A002378(n-1) + A144437(n+2).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

G.f.: (1 +x -x^3 +5*x^4)/( (1 +x +x^2)*(1 -x)^3 ).

E.g.f.: (1/3)*((7+3*x^2)*exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2)). - G. C. Greubel, Aug 24 2017

Extensions

Edited and extended by R. J. Mathar, Aug 12 2009