A282850 38-gonal numbers: a(n) = n*(18*n-17).

0, 1, 38, 111, 220, 365, 546, 763, 1016, 1305, 1630, 1991, 2388, 2821, 3290, 3795, 4336, 4913, 5526, 6175, 6860, 7581, 8338, 9131, 9960, 10825, 11726, 12663, 13636, 14645, 15690, 16771, 17888, 19041, 20230, 21455, 22716, 24013, 25346, 26715, 28120, 29561

Offset: 0

Author

Haney Moon, Feb 23 2017

Keywords

• nonn
• easy

Links

• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A255187, A254474, A261191.

Programs

Mathematica

Table[n(36n-34)/2, {n,50}]
LinearRecurrence[{3, -3, 1}, {0, 1, 38}, 42] (* or *) CoefficientList[Series[-x * (35 * x + 1) / (x - 1) ^ 3, {x, 0, 41}], x] (* Indranil Ghosh, Feb 27 2017 *)

PARI

for(n=0,20,print1(n*(18*n-17),", ")) \\ Derek Orr, Feb 26 2017

PARI

a(n)=n*(18*n-17) \\ Charles R Greathouse IV, Feb 26 2017

Formula

G.f.: -x*(35*x+1)/(x-1)^3.

E.g.f.: exp(x)*(x + 18*x^2). - Nikolaos Pantelidis, Feb 10 2023