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

Author

Colin Barker, Apr 28 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000384, A060544, A272398 (union).

Programs

Mathematica

Rest@ CoefficientList[Series[x (1 + 25 x + 10 x^2)/(1 - x)^3, {x, 0, 42}], x] (* Michael De Vlieger, Apr 28 2016 *)
LinearRecurrence[{3,-3,1},{1,28,91},50] (* Harvey P. Dale, Nov 08 2024 *)

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

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