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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 August 5 07:14 EDT 2021. Contains 346459 sequences. (Running on oeis4.)