

A051062


a(n) = 16*n + 8.


13



8, 24, 40, 56, 72, 88, 104, 120, 136, 152, 168, 184, 200, 216, 232, 248, 264, 280, 296, 312, 328, 344, 360, 376, 392, 408, 424, 440, 456, 472, 488, 504, 520, 536, 552, 568, 584, 600, 616, 632, 648, 664, 680, 696, 712, 728, 744, 760, 776, 792, 808, 824, 840
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OFFSET

0,1


COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0(97).
n such that 32 is the largest power of 2 dividing A003629(k)^n1 for any k.  Benoit Cloitre, Mar 23 2002
Continued fraction expansion of tanh(1/8).  Benoit Cloitre, Dec 17 2002
If Y and Z are 2blocks of a (4n+1)set X then a(n1) is the number of 3subsets of X intersecting both Y and Z.  Milan Janjic, Oct 28 2007
General form: (q*n+x)*q x=+1; q=2=A016825, q=3=A017197, q=4=A119413, ... x=1; q=3=A017233, q=4=A098502, ... x=+2; q=4=A051062, ...  Vladimir Joseph Stephan Orlovsky, Feb 16 2009
A003484(a(n)) = 8; A209675(a(n)) = 9.  Reinhard Zumkeller, Mar 11 2012
A007814(a(n)) = 3; A037227(a(n)) = 7.  Reinhard Zumkeller, Jun 30 2012
a(n)*n+1 = (4n+1)^2 and a(n)*(n+1)+1 = (4n+3)^2 are both perfect squares.  Carmine Suriano, Jun 01 2014
For all positive integers n, there are infinitely many positive integers k such that k*n + 1 and k*(n+1) + 1 are both perfect squares. Except for 8, all the numbers of this sequence are the smallest integers k which are solutions for getting two perfect squares. Example: a(1) = 24 and 24 * 1 + 1 = 25 = 5^2, then 24 * (1+1) + 1 = 49 = 7^2. [Reference AMM]  Bernard Schott, Sep 24 2017
Numbers k such that 3^k + 1 is divisible by 17*193.  Bruno Berselli, Aug 22 2018
Numbers that have three times as many even divisors as odd divisors.  Paolo P. Lava, Oct 17 2018


REFERENCES

Letter from Gary W. Adamson concerning ProuhetThueMorse sequence, Nov 11 1999


LINKS

Table of n, a(n) for n=0..52.
Mihaly Bencze, Problem 11508, The American Mathematical Monthly, Vol. 117, N° 5, May 2010, p. 459.
Milan Janjic, Two Enumerative Functions
Tanya Khovanova, Recursive Sequences
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))
William A. Stein, The modular forms database
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n) = A118413(n+1,4) for n>3.  Reinhard Zumkeller, Apr 27 2006
a(n) = 32*n  a(n1) for n>0, a(0)=8.  Vincenzo Librandi, Aug 06 2010
a(1  n) =  a(n).  Michael Somos, Jun 02 2014
a(n) = 2*A017113(n)  Paolo P. Lava, Oct 17 2018


MAPLE

A051062:=n>16*n+8; seq(A051062(n), n=0..50); # Wesley Ivan Hurt, Jun 01 2014


MATHEMATICA

Range[8, 1000, 16] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
Table[16n+8, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 01 2014 *)
LinearRecurrence[{2, 1}, {8, 24}, 60] (* or *) NestList[#+16&, 8, 60] (* Harvey P. Dale, Aug 18 2019 *)


PROG

(MAGMA) [16*n+8: n in [0..50]]; // Wesley Ivan Hurt, Jun 01 2014
(PARI) a(n)=16*n+8 \\ Charles R Greathouse IV, May 09 2016


CROSSREFS

Cf. A008598, A119413, A106839, A017113.
Sequence in context: A050427 A031046 A173080 * A152531 A074348 A063403
Adjacent sequences: A051059 A051060 A051061 * A051063 A051064 A051065


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Gary W. Adamson, Dec 11 1999


STATUS

approved



