A166137 a(n) = 5*n*(n+1)/2 - 4.

1, 11, 26, 46, 71, 101, 136, 176, 221, 271, 326, 386, 451, 521, 596, 676, 761, 851, 946, 1046, 1151, 1261, 1376, 1496, 1621, 1751, 1886, 2026, 2171, 2321, 2476, 2636, 2801, 2971, 3146, 3326, 3511, 3701, 3896, 4096, 4301, 4511, 4726, 4946, 5171, 5401, 5636

Offset: 1

Author

Vincenzo Librandi, Oct 08 2009

Keywords

• nonn
• easy

Comments

Numbers of the form 5*(h+1)*(2*h-1) + 1, where h = 0, -1, 1, -2, 2, -3, 3, -4, 4, ... . - Bruno Berselli, Feb 03 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A166151.

Programs

Magma

I:=[1,11,26]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 15 2012

Magma

[5*n*(n+1)/2-4: n in [0..40]]; // Bruno Berselli, Feb 03 2017

Maple

A166137:=n->5*n*(n+1)/2-4; seq(A166137(n), n=1..100); # Wesley Ivan Hurt, Nov 12 2013

Mathematica

LinearRecurrence[{3, -3, 1}, {1, 11, 26}, 50] (* Vincenzo Librandi, Mar 15 2012 *)
Table[5 n (n + 1)/2 - 4, {n, 47}] (* or *)
Rest@ CoefficientList[Series[x (-1 - 8 x + 4 x^2)/(x - 1)^3, {x, 0, 47}], x] (* Michael De Vlieger, Apr 27 2016 *)

PARI

for(n=1, 40, print1(5*n*(n+1)/2-4", ")); \\ Vincenzo Librandi, Mar 15 2012

Formula

a(n) = a(n-1) + 5*n = 3*a(n-1) - 3*a(n-2) + a(n-3) = A166151(n)-1.

O.g.f.: x*(-1 - 8*x + 4*x^2)/(x - 1)^3. [corrected by Georg Fischer, May 11 2019]

E.g.f.: (1/2)*(-8 + 10*x + 5*x^2)*exp(x). - G. C. Greubel, Apr 26 2016

Sum_{n>=1} 1/a(n) = 1/4 + (2*Pi/sqrt(185))*tan(sqrt(37/5)*Pi/2). - Amiram Eldar, Feb 20 2023

Extensions

Definition replaced by polynomial from R. J. Mathar, Oct 12 2009