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A157474 a(n) = 16n^2 + n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

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

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 *)

PROG

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

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

CROSSREFS

Cf. A157475, A157476.

Sequence in context: A115295 A065011 A031432 * A024215 A095071 A095072

Adjacent sequences:  A157471 A157472 A157473 * A157475 A157476 A157477

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 01 2009

EXTENSIONS

Comment rewritten by Bruno Berselli, Aug 22 2011

STATUS

approved

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Last modified October 6 21:32 EDT 2022. Contains 357270 sequences. (Running on oeis4.)