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A014634 a(n) = (2*n+1)*(4*n+1). 20
1, 15, 45, 91, 153, 231, 325, 435, 561, 703, 861, 1035, 1225, 1431, 1653, 1891, 2145, 2415, 2701, 3003, 3321, 3655, 4005, 4371, 4753, 5151, 5565, 5995, 6441, 6903, 7381, 7875, 8385, 8911, 9453, 10011, 10585, 11175, 11781, 12403, 13041, 13695, 14365, 15051 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Odd hexagonal numbers. Bisection of A000384. - Omar E. Pol, Apr 06 2008

Sequence found by reading the line from 1, in the direction 1, 15,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 03 2011

a(n) is also the sum of natural numbers which can be placed in a center box and expanded ones on 4 arms on N, S, E, W or NE, NW, SW, SE directions. See illustration in links. - Kival Ngaokrajang, Jul 08 2014

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Kival Ngaokrajang, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = A157870(n)/2. - Vladimir Joseph Stephan Orlovsky, Mar 10 2009

a(n) = a(n-1)+16*n-2 (with a(0)=1). - Vincenzo Librandi, Nov 20 2010

G.f.: (1+12*x+3*x^2)/(1-x)^3. - Colin Barker, Jan 08 2012

a(n) = A005408(n) * A016813(n). - Omar E. Pol, Nov 05 2013

a(n) = 2*A033954(n) + 1 = A194268(n) - n. - Wesley Ivan Hurt, Jul 14 2014

E.g.f.: (8*x^2 +14*x + 1)*exp(x). - G. C. Greubel, Jul 18 2017

MAPLE

A014634:=n->(2*n+1)*(4*n+1); seq(A014634(k), k=0..100); # Wesley Ivan Hurt, Nov 04 2013

MATHEMATICA

lst={}; Do[a=(2*n+1)*(4*n+1); AppendTo[lst, a], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 10 2009 *)

Table[(2 n + 1) (4 n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Jul 09 2014 *)

PROG

(MAGMA) [(2*n+1)*(4*n+1) : n in [0..50]]; // Wesley Ivan Hurt, Jul 09 2014

(PARI) a(n)=(2*n+1)*(4*n+1) \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000384.

Sequence in context: A033849 A194715 A060536 * A303857 A278337 A270563

Adjacent sequences:  A014631 A014632 A014633 * A014635 A014636 A014637

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian, N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, Jul 09 2014

STATUS

approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)