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A051874
22-gonal numbers: a(n) = n*(10*n-9).
11
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
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 22-gonal 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
This is also a star hendecagonal number: a(n) = A051682(n) + 11*A000217(n-1). - Luciano Ancora, Mar 30 2015
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
FORMULA
a(n) = 2*a(n-1)-a(n-2)+20 with n>1, a(0)=0, a(1)=1. - Zerinvary Lajos, Feb 18 2008
a(n) = 20*n+a(n-1)-19 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010
G.f.: x*(1+19*x)/(1-x)^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
Product_{n>=2} (1 - 1/a(n)) = 10/11. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 10*x^2). - Nikolaos Pantelidis, Feb 05 2023
MAPLE
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+20 od: seq(a[n], n=0..39); # Zerinvary Lajos, Feb 18 2008
MATHEMATICA
Table[n (10 n -9), {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*n-9) \\ Charles R Greathouse IV, Jan 24 2014
CROSSREFS
Sequence in context: A216299 A255431 A221595 * A140390 A069178 A081929
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 15 1999
STATUS
approved