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A179986 Second 9-gonal (or nonagonal) numbers: a(n) = n*(7*n+5)/2. 17
0, 6, 19, 39, 66, 100, 141, 189, 244, 306, 375, 451, 534, 624, 721, 825, 936, 1054, 1179, 1311, 1450, 1596, 1749, 1909, 2076, 2250, 2431, 2619, 2814, 3016, 3225, 3441, 3664, 3894, 4131, 4375, 4626, 4884, 5149, 5421, 5700, 5986, 6279, 6579, 6886 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence is a bisection of A118277 (even part).

Sequence found by reading the line from 0, in the direction 0, 19... and the line from 6, in the direction 6, 39,..., in the square spiral whose vertices are the generalized 9-gonal numbers A118277. - Omar E. Pol, Jul 24 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: x*(6 + x)/(1 - x)^3.

a(n) = Sum_{i=0..(n-1)} A017053(i) for n>0.

a(-n) = A001106(n).

Sum_{i=0..n} (a(n)+i)^2 = ( Sum_{i=(n+1)..2*n} (a(n)+i)^2 ) + 21*A000217(n)^2 for n>0.

a(n) = a(n-1)+7*n-1 for n>0, with a(0)=0. - Vincenzo Librandi, Feb 05 2011

a(0)=0, a(1)=6, a(2)=19; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Aug 19 2011

a(n) = A174738(7n+5). - Philippe Deléham, Mar 26 2013

a(n) = A001477(n) + 2*A000290(n) + 3*A000217(n). - J. M. Bergot, Apr 25 2014

a(n) = A055998(4*n) - A055998(3*n). - Bruno Berselli, Sep 23 2016

E.g.f.: (x/2)*(12 + 7*x)*exp(x). - G. C. Greubel, Aug 19 2017

MATHEMATICA

f[n_] := n (7 n + 5)/2; f[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)

LinearRecurrence[{3, -3, 1}, {0, 6, 19}, 60] (* or *) Array[(#(7# + 5))/2&, 60, 0] (* Harvey P. Dale, Aug 19 2011 *)

CoefficientList[Series[x (6 + x)/(1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 15 2012 *)

PROG

(MAGMA) [n*(7*n+5)/2: n in [0..50]]; // Bruno Berselli, Sep 23 2016

(MAGMA) I:=[0, 6, 19]; [n le 3 select I[n] else 3*Self(n-1) -3*Self(n-2) +Self(n-3): n in [1..60]]; // Vincenzo Librandi, Oct 15 2012

(PARI) a(n)=n*(7*n+5)/2 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. second k-gonal numbers: A005449 (k=5), A014105 (k=6), A147875 (k=7), A045944 (k=8), this sequence (k=9), A033954 (k=10), A062728 (k=11), A135705 (k=12).

Cf. A001106, A022264, A022265, A024966, A055998, A174738, A186029, A218471.

Sequence in context: A010899 A090381 A106398 * A054567 A096957 A272811

Adjacent sequences:  A179983 A179984 A179985 * A179987 A179988 A179989

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Jan 13 2011

STATUS

approved

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Last modified November 15 10:08 EST 2018. Contains 317233 sequences. (Running on oeis4.)