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

0,3

Comments

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

Links

Table of n, a(n) for n=0..39.

Index to sequences related to polygonal numbers

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

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)

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 *)

Prog

(Python)
for n in range(0, 51):
    print(n*(35*n-33)//2)
(PARI) for(n=0, 100, print1(n*(35*n-33)/2, ", ")) \\ Derek Orr, Feb 27 2017

Crossrefs

Cf. A254474, A000217.

Sequence in context: A005107 A139934 A142051 * A171833 A257117 A033215

Adjacent sequences: A282849 A282850 A282851 * A282853 A282854 A282855

Keyword

nonn,easy

Author

Nathan John Eaves, Feb 23 2017

Status

approved