A282852 37-gonal numbers: a(n) = n*(35*n-33)/2.

0, 1, 37, 108, 214, 355, 531, 742, 988, 1269, 1585, 1936, 2322, 2743, 3199, 3690, 4216, 4777, 5373, 6004, 6670, 7371, 8107, 8878, 9684, 10525, 11401, 12312, 13258, 14239, 15255, 16306, 17392, 18513, 19669, 20860, 22086, 23347, 24643, 25974

Offset: 0

Author

Nathan John Eaves, Feb 23 2017

Keywords

• nonn
• easy

Comments

According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 37).

Links

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

Crossrefs

Cf. A254474, A000217.

Programs

Mathematica

Table[n(35n-33)/2, {n, 40}]
PolygonalNumber[37,Range[0,40]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,1,37},40] (* Harvey P. Dale, Oct 24 2020 *)

PARI

for(n=0,100,print1(n*(35*n-33)/2,", ")) \\ Derek Orr, Feb 27 2017

Python

for n in range(0,51):
    print(n*(35*n-33)//2)

Formula

From Nikolaos Pantelidis, Feb 10 2023: (Start)

G.f.: x*(1 + 34*x)/(1 - x)^3.

E.g.f.: exp(x)*(x + 35*x^2/2). (End)