A051874 22-gonal numbers: a(n) = n*(10*n-9).

0, 1, 22, 63, 124, 205, 306, 427, 568, 729, 910, 1111, 1332, 1573, 1834, 2115, 2416, 2737, 3078, 3439, 3820, 4221, 4642, 5083, 5544, 6025, 6526, 7047, 7588, 8149, 8730, 9331, 9952, 10593, 11254, 11935, 12636, 13357, 14098, 14859

Offset

0,3

Comments

Sequence found by reading the line from 0, in the direction 0, 22,... and the parallel line from 1, in the direction 1, 63,..., in the square spiral whose vertices are the generalized 22-gonal numbers. - Omar E. Pol, Jul 18 2012

Also sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 22,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 29 2012

This is also a star hendecagonal number: a(n) = A051682(n) + 11*A000217(n-1). - Luciano Ancora, Mar 30 2015

References

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index to sequences related to polygonal numbers

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

Formula

a(n) = 2*a(n-1)-a(n-2)+20 with n>1, a(0)=0, a(1)=1. - Zerinvary Lajos, Feb 18 2008

a(n) = 20*n+a(n-1)-19 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010

G.f.: x*(1+19*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(20*a(n)+191*n+1) = a(20*a(n)+191*n) + a(20*n+1). - Vladimir Shevelev, Jan 24 2014

Product_{n>=2} (1 - 1/a(n)) = 10/11. - Amiram Eldar, Jan 22 2021

E.g.f.: exp(x)*(x + 10*x^2). - Nikolaos Pantelidis, Feb 05 2023

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+20 od: seq(a[n], n=0..39); # Zerinvary Lajos, Feb 18 2008

Mathematica

Table[n (10 n -9), {n, 0, 40}] (* Harvey P. Dale, Sep 19 2011 *)
CoefficientList[Series[x (1 + 19 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)

Prog

(PARI) a(n)=n*(10*n-9) \\ Charles R Greathouse IV, Jan 24 2014

Crossrefs

Sequence in context: A216299 A255431 A221595 * A140390 A069178 A081929

Adjacent sequences: A051871 A051872 A051873 * A051875 A051876 A051877

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 15 1999

Status

approved