A298784 Expansion of (1 + x^2)*(1 + 3*x + x^2) / ((1 - x)*(1 - x^3)).

1, 4, 6, 10, 14, 16, 20, 24, 26, 30, 34, 36, 40, 44, 46, 50, 54, 56, 60, 64, 66, 70, 74, 76, 80, 84, 86, 90, 94, 96, 100, 104, 106, 110, 114, 116, 120, 124, 126, 130, 134, 136, 140, 144, 146, 150, 154, 156, 160, 164, 166, 170, 174, 176, 180, 184, 186, 190, 194, 196, 200, 204, 206, 210, 214, 216, 220

Offset

0,2

Comments

Appears to be the coordination sequence for a tetravalent node in the bex tiling (or net).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Reticular Chemistry Structure Resource (RCSR), The bex tiling (or net)

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

a(0)=1; thereafter, a(3*k) = 10*k, a(3*k+1) = 10*k+4, a(3*k+2) = 10*k+6.

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Colin Barker, Jan 27 2018

Maple

f4:=proc(n)
if n=0 then 1
              elif (n mod 3) = 0 then 10*n/3
              elif (n mod 3) = 1 then (10*n+2)/3
              else (10*n-2)/3; fi; end;
[seq(f4(n), n=0..80)];

Prog

(PARI) Vec((1 + x^2)*(1 + 3*x + x^2) / ((1 - x)^2*(1 + x + x^2)) + O(x^100)) \\ Colin Barker, Jan 27 2018

Crossrefs

Cf. A298785, A298786.

Sequence in context: A134624 A171945 A310583 * A241975 A063745 A123666

Adjacent sequences: A298781 A298782 A298783 * A298785 A298786 A298787

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 26 2018

Status

approved