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A069128 Centered 15-gonal numbers: (15*n^2 - 15*n + 2)/2. 6
1, 16, 46, 91, 151, 226, 316, 421, 541, 676, 826, 991, 1171, 1366, 1576, 1801, 2041, 2296, 2566, 2851, 3151, 3466, 3796, 4141, 4501, 4876, 5266, 5671, 6091, 6526, 6976, 7441, 7921, 8416, 8926, 9451, 9991, 10546, 11116, 11701, 12301, 12916, 13546, 14191, 14851, 15526 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Centered pentadecagonal numbers or centered quindecagonal numbers or centered pentakaidecagonal numbers. - Omar E. Pol, Oct 03 2011

LINKS

T. D. Noe, 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) = (15*n^2 - 15*n + 2)/2.

a(n) = 15*n+a(n-1)-15 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010

G.f.: -x*(1+13*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011

Binomial transform of [1, 15, 15, 0, 0, 0, ...] and Narayana transform (A001263) of [1, 15, 0, 0, 0, ...]. - Gary W. Adamson, Jul 28 2011

a(n) = A194715(n-1) + 1. - Omar E. Pol, Oct 03 2011

EXAMPLE

a(5) = 151 because (15*5^2 - 15*5 + 2)/2 = (375 - 75 + 2)/2 = 302/2 = 151.

For n=2, a(2)=15*2+1-15=16; n=3, a(3)=15*3+16-15=46; n=4, a(4)=15*4+46-15=91. - Vincenzo Librandi, Aug 08 2010

MAPLE

A069128:=n->(15*n^2 - 15*n + 2)/2: seq(A069128(n), n=1..50); # Wesley Ivan Hurt, Nov 14 2014

MATHEMATICA

FoldList[#1 + #2 &, 1, 15 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)

LinearRecurrence[{3, -3, 1}, {1, 16, 46}, 50] (* Harvey P. Dale, Oct 22 2013 *)

PROG

(MAGMA) [(15*n^2 - 15*n + 2)/2 : n in [1..50]]; // Wesley Ivan Hurt, Nov 14 2014

(PARI) a(n)=15*n*(n-1)/2+1 \\ Charles R Greathouse IV, Nov 15 2014

CROSSREFS

Cf. A005448, A001844, A005891, A003215, A069099.

Sequence in context: A244343 A235772 A235555 * A099003 A124709 A244094

Adjacent sequences:  A069125 A069126 A069127 * A069129 A069130 A069131

KEYWORD

easy,nice,nonn

AUTHOR

Terrel Trotter, Jr., Apr 07 2002

STATUS

approved

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Last modified May 29 01:07 EDT 2017. Contains 287241 sequences.