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A069127 Centered 14-gonal numbers. 8
1, 15, 43, 85, 141, 211, 295, 393, 505, 631, 771, 925, 1093, 1275, 1471, 1681, 1905, 2143, 2395, 2661, 2941, 3235, 3543, 3865, 4201, 4551, 4915, 5293, 5685, 6091, 6511, 6945, 7393, 7855, 8331, 8821, 9325, 9843, 10375, 10921, 11481, 12055, 12643, 13245 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Binomial transform of [1, 14, 14, 0, 0, 0,...] and Narayana transform (A001263) of [1, 14, 0, 0, 0,...]. - Gary W. Adamson, Jul 29 2011

Centered tetradecagonal numbers or centered tetrakaidecagonal numbers. - Omar E. Pol, Oct 03 2011

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, 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) = 7*n^2 - 7*n + 1.

a(n) = 14*n+a(n-1)-14 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010

G.f.: -x*(1+12*x+x^2) / (x-1)^3. - R. J. Mathar, Feb 04 2011

a(n) = A163756(n-1) + 1. - Omar E. Pol, Oct 03 2011

a(n) = a(-n+1) = A193053(2n-2) + A193053(2n-3). - Bruno Berselli, Oct 21 2011

EXAMPLE

a(5) = 141 because 7*5^2 - 7*5 + 1 = 175 - 35 + 1 = 141.

a(5) = 71 because 71 = (7*5^2 - 7*5 + 2)/2 = (175 - 35 + 2)/2 = 142/2.

From Bruno Berselli, Oct 27 2017: (Start)

1   =         -(1) + (2).

15  =       -(1+2) + (3+4+5+6).

43  =     -(1+2+3) + (4+5+6+7+8+9+10).

85  =   -(1+2+3+4) + (5+6+7+8+9+10+11+12+13+14).

141 = -(1+2+3+4+5) + (6+7+8+9+10+11+12+13+14+15+16+17+18). (End)

MATHEMATICA

FoldList[#1 + #2 &, 1, 14 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)

Accumulate[14*Range[0, 50]]+1 (* Harvey P. Dale, Apr 09 2012 *)

PROG

(PARI) a(n)=7*n^2-7*n+1 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

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

Sequence in context: A280232 A233302 A072119 * A137183 A173873 A124708

Adjacent sequences:  A069124 A069125 A069126 * A069128 A069129 A069130

KEYWORD

nonn,easy,nice

AUTHOR

Terrel Trotter, Jr., Apr 07 2002

STATUS

approved

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Last modified November 18 19:06 EST 2017. Contains 294894 sequences.