

A051874


22gonal numbers: n(10n9).


4



0, 1, 22, 63, 124, 205, 306, 427, 568, 729, 910, 1111, 1332, 1573, 1834, 2115, 2416, 2737, 3078, 3439, 3820, 4221, 4642, 5083, 5544, 6025, 6526, 7047, 7588, 8149, 8730, 9331, 9952, 10593, 11254, 11935, 12636, 13357, 14098, 14859
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OFFSET

0,3


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 22,... and the parallel line from 1, in the direction 1, 63,..., in the square spiral whose vertices are the generalized 22gonal numbers.  Omar E. Pol, Jul 18 2012
Also sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 22,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787.  Omar E. Pol, Jul 29 2012


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = n(10n9).
a(n) = 2*a(n1)a(n2)+20 with n>1, a(0)=0, a(1)=1.  Zerinvary Lajos, Feb 18 2008
a(n) = 20*n+a(n1)19 with n>0, a(0)=0.  Vincenzo Librandi, Aug 06 2010
G.f.: x*(1+19*x)/(1x)^3.  Bruno Berselli, Feb 04 2011
a(20*a(n)+191*n+1) = a(20*a(n)+191*n) + a(20*n+1).  Vladimir Shevelev, Jan 24 2014


MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n1]a[n2]+20 od: seq(a[n], n=0..39); # Zerinvary Lajos, Feb 18 2008


MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 20}]; lst [Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
Table[n(10n9), {n, 0, 40}] (* Harvey P. Dale, Sep 19 2011 *)
CoefficientList[Series[x (1 + 19 x) / (1  x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)


PROG

(PARI) a(n)=n*(10*n9) \\ Charles R Greathouse IV, Jan 24 2014


CROSSREFS

Cf. ngonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865A051873, this sequence, A081875, A051876.
Sequence in context: A156797 A216299 A221595 * A140390 A069178 A081929
Adjacent sequences: A051871 A051872 A051873 * A051875 A051876 A051877


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Dec 15 1999


STATUS

approved



