

A298784


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


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
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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(n1) + a(n3)  a(n4) 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*n2)/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



