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A195162 Generalized 12-gonal numbers: k*(5*k-4) for k = 0, +-1, +-2, ... 51
0, 1, 9, 12, 28, 33, 57, 64, 96, 105, 145, 156, 204, 217, 273, 288, 352, 369, 441, 460, 540, 561, 649, 672, 768, 793, 897, 924, 1036, 1065, 1185, 1216, 1344, 1377, 1513, 1548, 1692, 1729, 1881, 1920, 2080, 2121, 2289, 2332, 2508, 2553, 2737, 2784, 2976, 3025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also generalized dodecagonal numbers.

Second 12-gonal numbers (A135705) and positive terms of A051624 interleaved. - Omar E. Pol, Aug 04 2012

The characteristic function of this sequence is A205988. - Jason Kimberley, Nov 15 2012

Also, integer values of m*(m+4)/5. - Bruno Berselli, Dec 05 2012

Also, numbers h such that 5*h + 4 is a square. - Bruno Berselli, Oct 10 2013

LINKS

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

S. Cooper and M. D. Hirschhorn, Results of Hurwitz type for three squares. Discrete Math. 274 (2004), no. 1-3, 9-24. See E(q).

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

FORMULA

From R. J. Mathar, Sep 24 2011: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

a(n) = A008805(n-1)+A008805(n-3)+8*A008805(n-2). (End)

From Bruno Berselli, Sep 26 2011: (Start)

G.f.: x*(1+8*x+x^2)/((1+x)^2*(1-x)^3).

a(n) = (10*n*(n+1)+3*(2*n+1)*(-1)^n-3)/8.

a(n) = a(-n-1). (End)

Sum_{n>=1} 1/a(n) = (5 + 4*sqrt(1 + 2/sqrt(5))*Pi)/16. - Vaclav Kotesovec, Oct 05 2016

MATHEMATICA

nn = 25; Sort[Table[n*(5*n - 4), {n, -nn, nn}]] (* T. D. Noe, Sep 23 2011 *)

PROG

(MAGMA) [0] cat &cat[[5*n^2-4*n, 5*n^2+4*n]: n in [1..25]]; // Vincenzo Librandi, Sep 26 2011

CROSSREFS

Partial sums of A195161.

Column 8 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), this sequence (k=12), A195313 (k=13), A195818 (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).

Cf. A051624, A135705.

Cf. sequences of the form m*(m+k)/(k+1) listed in A274978. [Bruno Berselli, Jul 25 2016]

Sequence in context: A114434 A105704 A216192 * A216297 A024312 A024877

Adjacent sequences:  A195159 A195160 A195161 * A195163 A195164 A195165

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 10 2011

STATUS

approved

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Last modified October 20 04:37 EDT 2018. Contains 316378 sequences. (Running on oeis4.)