A104099 a(n) = n * (10*n^2 - 6n + 1) = n * A087348(n).

0, 5, 58, 219, 548, 1105, 1950, 3143, 4744, 6813, 9410, 12595, 16428, 20969, 26278, 32415, 39440, 47413, 56394, 66443, 77620, 89985, 103598, 118519, 134808, 152525, 171730, 192483, 214844, 238873, 264630, 292175, 321568, 352869, 386138, 421435

Offset: 0

Author

Roger L. Bagula, Mar 31 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Maple

a[0]:=0:a[1]:=5:a[2]:=58:a[3]:=219: for n from 4 to 40 do a[n]:=4*a[n-1]-6*a[n-2]+4*a[n-3]-a[n-4] od: seq(a[n], n=0..40);

Mathematica

Table[n(10n^2-6n+1),{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,5,58,219},40] (* Harvey P. Dale, Sep 01 2018 *)

PARI

a(n)=n*(10*n^2 - 6*n + 1) \\ Charles R Greathouse IV, Oct 18 2022

Formula

Recurrence relation: a(n)=4a(n-1)-6a(n-2)+4a(n-3)-a(n-4) for n>=4; a(0)=0, a(1)=5, a(2)=58, a(3)=219.

O.g.f.: x*(5+38*x+17*x^2)/(-1+x)^4 = 132/(-1+x)^3+60/(-1+x)^4+89/(-1+x)^2+17/(-1+x) . - R. J. Mathar, Dec 05 2007

Extensions

Edited by N. J. A. Sloane, May 20 2006, Jun 06 2007