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A069133 Centered 20-gonal (or icosagonal) numbers. 13
1, 21, 61, 121, 201, 301, 421, 561, 721, 901, 1101, 1321, 1561, 1821, 2101, 2401, 2721, 3061, 3421, 3801, 4201, 4621, 5061, 5521, 6001, 6501, 7021, 7561, 8121, 8701, 9301, 9921, 10561, 11221, 11901, 12601, 13321, 14061, 14821, 15601, 16401, 17221, 18061 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equals binomial transform of [1, 20, 20, 0, 0, 0,...]. - Gary W. Adamson, Jun 13 2008

Equals Narayana transform (A001263) of [1, 20, 0, 0, 0,...]. - Gary W. Adamson, Jul 28 2011

Sequence found by reading the line from 1, in the direction 1, 21,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. Semi-axis opposite to A033583 in the same spiral. - Omar E. Pol, Sep 16 2011

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000

E. Weisstein, Centered Polygonal Numbers

Index entries for sequences related to centered polygonal numbers

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

FORMULA

a(n) = 10n^2 - 10n + 1.

a(n) = 20*n+a(n-1)-20 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010

G.f.: x*(1+18*x+x^2) / (1-x)^3 . - R. J. Mathar, Feb 04 2011

a(0)=1, a(1)=21, a(2)=61, a(n)=3a(n-1)-3a(n-2)+a(n-3). - Harvey P. Dale, Apr 29 2011

EXAMPLE

a(5)=201 because 201 = 10*5^2 - 10*5 + 1 = 250 - 50 + 1.

MATHEMATICA

FoldList[#1 + #2 &, 1, 20 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)

Table[10n^2-10n+1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 21, 61}, 50]  (* Harvey P. Dale, Apr 29 2011 *)

PROG

(PARI) a(n)=10*n*(n-1)+1 \\ Charles R Greathouse IV, Jul 29 2011

CROSSREFS

Cf. centered polygonal numbers listed in A069190.

Sequence in context: A051873 A223460 A219690 * A124714 A126375 A146468

Adjacent sequences:  A069130 A069131 A069132 * A069134 A069135 A069136

KEYWORD

easy,nice,nonn

AUTHOR

Terrel Trotter, Jr., Apr 07 2002

STATUS

approved

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Last modified August 23 00:16 EDT 2017. Contains 290953 sequences.