A157474 a(n) = 16n^2 + n.

17, 66, 147, 260, 405, 582, 791, 1032, 1305, 1610, 1947, 2316, 2717, 3150, 3615, 4112, 4641, 5202, 5795, 6420, 7077, 7766, 8487, 9240, 10025, 10842, 11691, 12572, 13485, 14430, 15407, 16416, 17457, 18530, 19635, 20772, 21941, 23142, 24375, 25640

Offset: 1

Author

Vincenzo Librandi, Mar 01 2009

Keywords

• nonn
• easy

Comments

The identity (2048*n^2+128*n+1)^2 - (16*n^2+n)*(512*n+16)^2 = 1 can be written as A157476(n)^2 - a(n)*A157475(n)^2 = 1 (see also second comment in A157476).

Sequence found by reading the line from 17, in the direction 17, 66,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012

Links

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

Crossrefs

Cf. A157475, A157476.

Programs

Magma

[16*n^2 + n: n in [1..40]]; // Vincenzo Librandi, Jan 01 2015

Mathematica

Table[16n^2+n,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{17,66,147},50] (* Harvey P. Dale, Nov 08 2011 *)
CoefficientList[Series[(17 + 14 x + 3 x^2 - 3 x^3 + x^4) / (1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 01 2015 *)

PARI

a(n)=16*n^2+n \\ Charles R Greathouse IV, Feb 09 2012

Formula

a(n) = A173511(2*n). - Reinhard Zumkeller, Feb 20 2010

a(1)=17, a(2)=66, a(3)=147, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Nov 08 2011

G.f.: x*(17 + 14*x + 3*x^2 - 3*x^3 + x^4)/(1-x)^3. - Vincenzo Librandi, Jan 01 2015

Extensions

Comment rewritten by Bruno Berselli, Aug 22 2011