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%I #20 Apr 29 2016 06:58:10
%S 1,28,91,190,325,496,703,946,1225,1540,1891,2278,2701,3160,3655,4186,
%T 4753,5356,5995,6670,7381,8128,8911,9730,10585,11476,12403,13366,
%U 14365,15400,16471,17578,18721,19900,21115,22366,23653,24976,26335,27730,29161,30628
%N The intersection of hexagonal numbers (A000384) and centered 9-gonal numbers (A060544).
%H Colin Barker, <a href="/A272399/b272399.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A272398(4*n-3).
%F a(n) = 10-27*n+18*n^2.
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
%F G.f.: x*(1+25*x+10*x^2) / (1-x)^3.
%F a(n) = A000384(3*n-2) = A060544(2*n-1). - _Robert Israel_, Apr 28 2016
%F E.g.f.: (9*x*(2*x - 1) + 10)*exp(x) - 10. - _Ilya Gutkovskiy_, Apr 28 2016
%t Rest@ CoefficientList[Series[x (1 + 25 x + 10 x^2)/(1 - x)^3, {x, 0, 42}], x] (* _Michael De Vlieger_, Apr 28 2016 *)
%o (PARI) lista(nn) = for(n=1, nn, print1(10-27*n+18*n^2, ", ")); \\ _Altug Alkan_, Apr 28 2016
%o (PARI) a(n)=18*n^2-27*n+10 \\ _Charles R Greathouse IV_, Apr 28 2016
%o (PARI) Vec(x*(1+25*x+10*x^2) / (1-x)^3 + O(x^50)) \\ _Colin Barker_, Apr 29 2016
%Y Cf. A000384, A060544, A272398 (union).
%K nonn,easy
%O 1,2
%A _Colin Barker_, Apr 28 2016
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