# [seqfan] "linear" class of sequences

юрий герасимов 2stepan at rambler.ru
Mon Jan 26 21:48:11 CET 2015

```Dear SeqFans.
Consider a class of sequences generated by the function
G(x, y, z) = (x*y + (3 + (-1)^x)/2)*z + x*y + (3 - (-1)^x)/2,
where
i  a(n) = G(x = n, y = constant, z = constant) = G(n, const, const);
ii  a(n) = G(x = constant, y = n, z = constant) = G(const, n, const);
iii  a(n) = G(x = constant, y = constant, z = n) = G(const, const, n).
Among the sequences in this class (for constant <= 3) are:
A000012(n) = G(0,n,0),
A000039(n) = G(n,0,0),
A004767(n) = G(2,1,n) = G(2,n,1) = G(n,2,1),
A004771(n) = G(2,n,3) = G(2,3,n),
A005408(n) = G(0,0,n) = G(0,1,n) = G(0,2,n) = G(2,0,n) = G(2,n,0) = G(0,3,n),
A007310(n) = G(n,1,2) = G(n,3,0),
A010701(n) = G(0,n,1) = G(n,0,1),
A010710(n) = G(n,0,2),
A010716(n) = G(0,n,2),
A010718(n) = G(n,0,3),
A016777(n) = G(1,2,n) = G(1,n,2),
A016789(n) = G(3,n,0),
A016813(n) = G(1,3,n) = G(3,1,n) = G(1,n,3),
A016945(n) = G(3,n,1) = G(n,3,1),
A016969(n) = G(2,2,n) = G(2,n,2),
A016993(n) = G(3,2,n),
A017209(n) = G(3,n,2),                                                                               ,
A017281(n) = G(3,3,n),
A017581(n) = G(3,n,3),
A020725(n) = G(1,0,n) = G(1,n,0) = G(3,0,n) = G(0,n,3),
A042948(n) = G(n,2,0),
A047522(n) = G(n,1,3),
A063196(n) = G(n,1,0),
A143988(n) = G(n,3,2),
A144396(n) = G(1,1,n) = G(1,n,1) = G(n,1,1),
Numbers congruent to -2 or 5 mod 12:  G(n,2,2),
Numbers congruent to 7 or 13 mod 16:  G(n,2,3),
Numbers congruent to 7 or 17 mod 24:  G(n,3,3).
The class could be called "linear". This may be very basic, but does a name for