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A014634 a(n) = (2*n+1)*(4*n+1). 24
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
Kival Ngaokrajang, Illustration of initial terms.
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
From Amiram Eldar, Feb 28 2022: (Start)
Sum_{n>=0} 1/a(n) = Pi/4 + log(2)/2.
Sum_{n>=0} (-1)^n/a(n) = Pi*(sqrt(2)-1)/4 + log(sqrt(2)+1)/sqrt(2). (End)
a(n) = A003154(n+1) + 2*A000290(n). - Leo Tavares, Mar 26 2022
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 *)
LinearRecurrence[{3, -3, 1}, {1, 15, 45}, 50] (* Harvey P. Dale, Aug 30 2021 *)
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
Sequence in context: A033849 A194715 A060536 * A303857 A278337 A270563
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, Jul 09 2014
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)