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A195818 Generalized 14-gonal numbers: n*(6*n-5), n = 0,+1,-1,+2,-2,+3,-3,... 25
0, 1, 11, 14, 34, 39, 69, 76, 116, 125, 175, 186, 246, 259, 329, 344, 424, 441, 531, 550, 650, 671, 781, 804, 924, 949, 1079, 1106, 1246, 1275, 1425, 1456, 1616, 1649, 1819, 1854, 2034, 2071, 2261, 2300, 2500, 2541, 2751, 2794, 3014, 3059, 3289 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also generalized tetradecagonal numbers or generalized tetrakaidecagonal numbers.

Also A211014 and positive terms of A051866 interleaved. - Omar E. Pol, Aug 04 2012

LINKS

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

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

FORMULA

a(n) = (3*n*(n+1)+(2*n+1)*(-1)^n-1)/2. - Vincenzo Librandi, Sep 30 2011

G.f.: -x*(x^2+10*x+1) / ((x-1)^3*(x+1)^2). - Colin Barker, Sep 15 2013

Sum_{n>=1} 1/a(n) = 6/25 + sqrt(3)*Pi/5. - Vaclav Kotesovec, Oct 05 2016

PROG

(MAGMA) [(3*n*(n+1)+(2*n+1)*(-1)^n-1)/2: n in [0..60]]; // Vincenzo Librandi, Sep 30 2011

(MAGMA) A195818:=func<n | n*(6*n-5)>; [0] cat [A195818(n*m): m in [1, -1], n in [1..25]];

(PARI) Vec(-x*(x^2+10*x+1)/((x-1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 15 2013

CROSSREFS

Partial sums of A195817. Column 10 of A195152.

Generalized k-gonal numbers, k>=5: A001318, A000217, A085787, A001082, A118277, A074377, A195160, A195162, A195313, this sequence.

Sequence in context: A045139 A043105 A043885 * A101840 A061087 A063964

Adjacent sequences:  A195815 A195816 A195817 * A195819 A195820 A195821

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 29 2011

STATUS

approved

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Last modified February 23 02:43 EST 2018. Contains 299473 sequences. (Running on oeis4.)