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A272399
The intersection of hexagonal numbers (A000384) and centered 9-gonal numbers (A060544).
5
1, 28, 91, 190, 325, 496, 703, 946, 1225, 1540, 1891, 2278, 2701, 3160, 3655, 4186, 4753, 5356, 5995, 6670, 7381, 8128, 8911, 9730, 10585, 11476, 12403, 13366, 14365, 15400, 16471, 17578, 18721, 19900, 21115, 22366, 23653, 24976, 26335, 27730, 29161, 30628
OFFSET
1,2
FORMULA
a(n) = A272398(4*n-3).
a(n) = 10-27*n+18*n^2.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
G.f.: x*(1+25*x+10*x^2) / (1-x)^3.
a(n) = A000384(3*n-2) = A060544(2*n-1). - Robert Israel, Apr 28 2016
E.g.f.: (9*x*(2*x - 1) + 10)*exp(x) - 10. - Ilya Gutkovskiy, Apr 28 2016
MATHEMATICA
Rest@ CoefficientList[Series[x (1 + 25 x + 10 x^2)/(1 - x)^3, {x, 0, 42}], x] (* Michael De Vlieger, Apr 28 2016 *)
PROG
(PARI) lista(nn) = for(n=1, nn, print1(10-27*n+18*n^2, ", ")); \\ Altug Alkan, Apr 28 2016
(PARI) a(n)=18*n^2-27*n+10 \\ Charles R Greathouse IV, Apr 28 2016
(PARI) Vec(x*(1+25*x+10*x^2) / (1-x)^3 + O(x^50)) \\ Colin Barker, Apr 29 2016
CROSSREFS
Cf. A000384, A060544, A272398 (union).
Sequence in context: A096384 A065655 A341623 * A113958 A219815 A044215
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Apr 28 2016
STATUS
approved