A261276 100-gonal numbers: a(n) = 98*n*(n-1)/2 + n.

0, 1, 100, 297, 592, 985, 1476, 2065, 2752, 3537, 4420, 5401, 6480, 7657, 8932, 10305, 11776, 13345, 15012, 16777, 18640, 20601, 22660, 24817, 27072, 29425, 31876, 34425, 37072, 39817, 42660, 45601, 48640, 51777, 55012, 58345, 61776, 65305, 68932, 72657, 76480

Offset

0,3

Comments

According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 100).

Links

Table of n, a(n) for n=0..40.

Index to sequences related to polygonal numbers

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

Formula

a(n) = n*(49*n - 48).

G.f.: x*(1+97*x)/(1-x)^3. [Bruno Berselli, Aug 20 2015]

E.g.f.: exp(x)*(x + 49*x^2). - Nikolaos Pantelidis, Feb 12 2023

Maple

A261276:=seq((98*n*(n-1))/2 + n, n=0..10^2); # Muniru A Asiru, Sep 27 2017

Mathematica

Table[n (49 n - 48), {n, 0, 40}] (* Bruno Berselli, Aug 20 2015 *)
PolygonalNumber[100, Range[0, 40]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 100}, 50] (* Harvey P. Dale, Jan 04 2019 *)

Prog

(JavaScript) function a(n){return 98*n*(n-1)/2+n}
(PARI) first(m)=vector(m, i, i--; 98*i*(i-1)/2 + i) \\ Anders Hellström, Aug 20 2015
(GAP)
A261276:=List([0..10^2], n->(98*n*(n-1))/2 + n); # Muniru A Asiru, Sep 27 2017

Crossrefs

Cf. A167149, A195163, A249911.

Sequence in context: A027604 A116145 A248550 * A104908 A109633 A124437

Adjacent sequences: A261273 A261274 A261275 * A261277 A261278 A261279

Keyword

nonn,easy

Author

Sergey Pavlov, Aug 13 2015

Status

approved