A272399 The intersection of hexagonal numbers (A000384) and centered 9-gonal numbers (A060544).

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

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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

Adjacent sequences: A272396 A272397 A272398 * A272400 A272401 A272402

Keyword

nonn,easy

Author

Colin Barker, Apr 28 2016

Status

approved