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A051062 16n+8. 10
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 (list; graph; refs; listen; history; text; internal format)
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)^n-1 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 2-blocks of a (4n+1)-set X then a(n-1) is the number of 3-subsets 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

REFERENCES

Letter from Gary W. Adamson concerning Prouhet-Thue-Morse sequence, Nov 11 1999

LINKS

Table of n, a(n) for n=0..52.

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(n-1), (with a(0)=8). - Vincenzo Librandi, Aug 06 2010

a(-1 - n) = - a(n). - Michael Somos, Jun 02 2014

EXAMPLE

a(1) = 32*1-8 = 24; a(2) = 32*2-24 = 40; a(3) = 32*3-40 = 56. - Vincenzo Librandi, Aug 06 2010

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 *)

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.

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

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Last modified August 23 00:16 EDT 2017. Contains 290953 sequences.