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A195818 Generalized 14-gonal numbers: m*(6*m-5), m = 0,+1,-1,+2,-2,+3,-3,... 42
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

MATHEMATICA

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 11, 14, 34}, 50] (* Harvey P. Dale, Mar 13 2018 *)

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.

Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), A195160 (k=11), A195162 (k=12), A195313 (k=13), this sequence (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).

Sequence in context: A043105 A043885 A305010 * 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 August 19 01:39 EDT 2018. Contains 313840 sequences. (Running on oeis4.)