A298786 Expansion of (x^4 + 2*x^3 + 4*x^2 + 2*x + 1) / ((1 - x)*(1 - x^3)).

1, 3, 7, 10, 13, 17, 20, 23, 27, 30, 33, 37, 40, 43, 47, 50, 53, 57, 60, 63, 67, 70, 73, 77, 80, 83, 87, 90, 93, 97, 100, 103, 107, 110, 113, 117, 120, 123, 127, 130, 133, 137, 140, 143, 147, 150, 153, 157, 160, 163, 167, 170, 173, 177, 180, 183, 187, 190, 193, 197, 200, 203, 207, 210, 213, 217

Offset

0,2

Comments

Appears to be the coordination sequence for a trivalent 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(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Colin Barker, Jan 27 2018

Maple

f3:=proc(n)
if n=0 then 1
              elif (n mod 3) = 0 then 10*n/3
              elif (n mod 3) = 1 then (10*n-1)/3
              else (10*n+1)/3; fi; end;
[seq(f3(n), n=0..80)];

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {1, 3, 7, 10, 13}, 100] (* Paolo Xausa, Jun 25 2025 *)

Prog

(PARI) Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^2*(1 + x + x^2)) + O(x^100)) \\ Colin Barker, Jan 27 2018

Crossrefs

Cf. A298784, A298787.

Sequence in context: A160591 A297466 A198267 * A285359 A255607 A310185

Adjacent sequences: A298783 A298784 A298785 * A298787 A298788 A298789

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 26 2018

Status

approved