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A195143 a(n) = n-th concentric 12-gonal number. 14
0, 1, 12, 25, 48, 73, 108, 145, 192, 241, 300, 361, 432, 505, 588, 673, 768, 865, 972, 1081, 1200, 1321, 1452, 1585, 1728, 1873, 2028, 2185, 2352, 2521, 2700, 2881, 3072, 3265, 3468, 3673, 3888, 4105, 4332, 4561, 4800, 5041, 5292, 5545, 5808, 6073, 6348 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also concentric dodecagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 12,..., and the same line from 1, in the direction 1, 25,..., in the square spiral whose vertices are the generalized octagonal numbers A001082. Main axis, perpendicular to A028896 in the same spiral.

Partial sums of A091998. - Reinhard Zumkeller, Jan 07 2012

Column 12 of A195040. - Omar E. Pol, Sep 28 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

From Vincenzo Librandi, Sep 27 2011: (Start)

a(n) = 3*n^2+(-1)^n-1.

a(n) = -a(n-1) + 6*n^2 - 6*n + 1. (End)

G.f.: -x*(1+10*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011

a(n) = sum_{k=1..n} (2*(-1)^(n-k+1) + 3*(2*k-1)), n>0, a(0) = 0. - L. Edson Jeffery, Sep 14 2014

MATHEMATICA

Table[Sum[2*(-1)^(n - k + 1) + 6*k - 3, {k, n}], {n, 0, 47}] (* L. Edson Jeffery, Sep 14 2014 *)

PROG

(MAGMA) [(3*n^2+(-1)^n-1): n in [0..50]]; // Vincenzo Librandi, Sep 27 2011

(Haskell)

a195143 n = a195143_list !! n

a195143_list = scanl (+) 0 a091998_list

-- Reinhard Zumkeller, Jan 07 2012

CROSSREFS

Cf. A135453 and A069190 interleaved.

Cf. A032527, A032528, A077221, A195043, A195045, A195040, A195142, A195145-A195149.

Cf. A016921 (6n+1), A016969 (6n+5), A091998 (positive integers of the form 12*k +- 1), A092242 (positive integers of the form 12*k +- 5).

Sequence in context: A250666 A224669 A164577 * A280321 A198274 A229447

Adjacent sequences:  A195140 A195141 A195142 * A195144 A195145 A195146

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 17 2011

EXTENSIONS

Comment corrected by Ivan Panchenko, Nov 09 2013

STATUS

approved

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Last modified July 22 05:05 EDT 2017. Contains 289648 sequences.