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%I A029136 #25 Jan 17 2024 12:05:11
%S A029136 1,0,1,1,2,1,4,2,5,4,7,5,11,7,13,11,17,13,23,17,27,23,33,27,42,33,48,
%T A029136 42,57,48,69,57,78,69,90,78,106,90,118,106,134,118,154,134,170,154,
%U A029136 190,170,215,190,235,215,260,235,290,260,315,290,345,315,381,345
%N A029136 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)).
%C A029136 Number of nonisomorphic hollow hexagons with n hexagons for n >= 8 (a class of primitive coronoids).
%C A029136 Number of partitions of n into parts 2, 3, 4, and 6. - _Joerg Arndt_, Jul 09 2014
%D A029136 B. N. Cyvin et al., Enumeration of conjugated hydrocarbons..., Structural Chem., 6 (1995), 85-88, equations (1)-(5) and (24).
%H A029136 Robert Israel, <a href="/A029136/b029136.txt">Table of n, a(n) for n = 0..10000</a>
%H A029136 Tricia Muldoon Brown, <a href="https://pisrt.org/psr-press/journals/odam-vol-6-issue-3-2023/lattice-path-coronoids/">Lattice path coronoids</a>, Open J. Disc. Appl. Math. (2023) Vol. 6, No. 3, 1-21.
%H A029136 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,-1,0,-1,-1,0,-1,1,1,1,0,-1).
%F A029136 a(n) = floor((2*n^3 + 45*n^2 + (273 + 96*(floor(n/3) - floor((n-1)/3)))*n + 1284 + 3*(3*n^2 + 45*n + 148)*(-1)^n)/1728). - _Tani Akinari_, Jul 08 2014
%F A029136 a(i+15) - a(i+13) - a(i+12) - a(i+11) + a(i+10) + a(i+8) + a(i+7) + a(i+5) - a(i+4) - a(i+3) - a(i+2) + a(i) = 0. - _Robert Israel_, Jul 08 2014
%p A029136 M := Matrix(15, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 4, 11, 12, 13])) then 1 elif j=1 and member(i, [5, 7, 8, 10, 15]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..53); # _Alois P. Heinz_, Jul 25 2008
%t A029136 CoefficientList[Series[1/((1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^6)), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Jul 08 2014 *)
%o A029136 (PARI) a(n)=(2*n^3+45*n^2+(273+96*(n%3<1))*n+1284+3*(3*n^2+45*n+148)*(-1)^n)\1728 \\ _Tani Akinari_, Jul 08 2014
%K A029136 nonn,easy
%O A029136 0,5
%A A029136 _N. J. A. Sloane_
%E A029136 More terms from _Wesley Ivan Hurt_, Jul 08 2014

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