OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Gregory Emmett Coxson and Jon Carmelo Russo, Enumeration and Generation of PSL Equivalence Classes for Quad-Phase Codes of Even Length, IEEE Transactions on Aerospace and Electronic Systems, Year: 2017, Volume: 53, Issue: 4, p. 1907-1915.
Vincent Pilaud and V. Pons, Permutrees, arXiv preprint arXiv:1606.09643 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (4,4,-16).
FORMULA
a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3) with n>2, a(0)=1, a(1)=3, a(2)=7 (communicated by Jon E. Schoenfield).
a(n) = 2^(n-3)*(2^(n+1) - (-1)^n + 7).
G.f.: (1-x-9*x^2)/((1-2*x)*(1+2*x)*(1-4*x)).
MATHEMATICA
LinearRecurrence[{4, 4, -16}, {1, 3, 7}, 30] (* Bruno Berselli, May 17 2013 *)
CoefficientList[Series[(1 - x - 9 x^2) / ((1 - 2 x) (1 + 2 x) (1 - 4 x)), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 03 2013 *)
PROG
(Magma) [2^(n-3)*(2^(n+1)-(-1)^n+7): n in [0..25]]; // Vincenzo Librandi, Sep 03 2013
CROSSREFS
Cf. A005418 = Number of binary pattern classes in the (1,n)-rectangular grid, A225826 to A225834 are the numbers of binary pattern classes in the (m,n)-rectangular grid, 1 < m < 11, A132390 is the sequence when the 90-degree rotation for pattern equivalence is allowed. So, only a(2) is different (communicated by Jon E. Schoenfield). See A054247 for (n,n)-grids.
A225910 is the table of (m,n)-rectangular grids.
KEYWORD
nonn,easy
AUTHOR
Yosu Yurramendi, May 16 2013
STATUS
approved