A180232 a(n) = n*(17*n - 13)/2.

0, 2, 21, 57, 110, 180, 267, 371, 492, 630, 785, 957, 1146, 1352, 1575, 1815, 2072, 2346, 2637, 2945, 3270, 3612, 3971, 4347, 4740, 5150, 5577, 6021, 6482, 6960, 7455, 7967, 8496, 9042, 9605, 10185, 10782, 11396, 12027, 12675, 13340, 14022, 14721, 15437, 16170

Offset: 0

Author

Graziano Aglietti (mg5055(AT)mclink.it), Aug 18 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A051871.

Cf. A226488. [Bruno Berselli, Jun 10 2013]

Programs

GAP

List([0..40], n-> n*(17*n-13)/2); # G. C. Greubel, Aug 30 2019

Magma

[n*(17*n-13)/2:n in [0..40]]; // Vincenzo Librandi, Sep 15 2011

Maple

seq(n*(17*n-13)/2, n=0..40); # G. C. Greubel, Aug 30 2019

Mathematica

Table[(n(17n-13))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1}, {0,2, 21}, 50] (* Harvey P. Dale, Sep 14 2011 *)

PARI

a(n)=1/2*(17*n^2 - 13*n);

Sage

[n*(17*n-13)/2 for n in (0..40)] # G. C. Greubel, Aug 30 2019

Formula

a(n) = n + A051871(n).

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

G.f.: x*(2+15*x)/(1-x)^3. - R. J. Mathar, Aug 29 2010

E.g.f.: x *(4 + 17*x)*exp(x)/2. - G. C. Greubel, Aug 30 2019

Extensions

More terms from R. J. Mathar, Aug 29 2010