A017569 a(n) = 12*n + 4.

4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 148, 160, 172, 184, 196, 208, 220, 232, 244, 256, 268, 280, 292, 304, 316, 328, 340, 352, 364, 376, 388, 400, 412, 424, 436, 448, 460, 472, 484, 496, 508, 520, 532, 544, 556, 568, 580, 592, 604, 616, 628

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(46).

Number of 6 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1A008574; m=3: A016933; m=4: A022144; m=5: A017293. - Sergey Kitaev, Nov 13 2004

Except for 4, exponents e such that x^e - x^2 + 1 is reducible.

If Y and Z are 2-blocks of a (3n+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

Terms are perfect squares iff n is a generalized octagonal number (A001082), then n = k*(3*k-2) and a(n) = (2*(3*k-1))^2. - Bernard Schott, Feb 26 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Milan Janjic, Two Enumerative Functions.
• Tanya Khovanova, Recursive Sequences.
• Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 4 (2004), Article A21, 20pp.
• William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
• William A. Stein, The modular forms database.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008594, A017533, A017545, A089911.

Cf. A016777, A016933, A017293, A022144.

Cf. A001082.

Programs

Haskell

a017569 = (+ 4) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

Magma

[12*n+4: n in [0..50]]; // Vincenzo Librandi, May 04 2011

Mathematica

12*Range[0,200]+4 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

Formula

A089911(a(n)) = 3. - Reinhard Zumkeller, Jul 05 2013

Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(2)/12. - Amiram Eldar, Dec 12 2021

From Stefano Spezia, Feb 25 2023: (Start)

O.g.f.: 4*(1 + 2*x)/(1 - x)^2.

E.g.f.: 4*exp(x)*(1 + 3*x). (End)

From Elmo R. Oliveira, Apr 10 2025: (Start)

a(n) = 2*a(n-1) - a(n-2).

a(n) = 2*A016933(n) = 4*A016777(n) = A016777(4*n+1). (End)