|
| |
|
|
A051624
|
|
12-gonal (or dodecagonal) numbers: n(5n-4).
|
|
51
|
|
|
|
0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729, 1920, 2121, 2332, 2553, 2784, 3025, 3276, 3537, 3808, 4089, 4380, 4681, 4992, 5313, 5644, 5985, 6336, 6697, 7068, 7449, 7840, 8241, 8652
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Zero followed by partial sums of A017281. [From Klaus Brockhaus, Nov 20 2008]
Sequence found by reading the line from 0, in the direction 0, 12,... and the parallel line from 1, in the direction 1, 33,..., in the square spiral whose vertices are the generalized 12-gonal numbers A195162. - Omar E. Pol, Jul 18 2012
|
|
|
REFERENCES
|
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
L. Hogben, Choice and Chance by Cardpack and Chessboard. Vol. 1, Chanticleer Press, NY, 1950, p. 36.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.
|
|
|
LINKS
|
T. D. Noe, 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*(5*n-4).
G.f.: x*(1+9*x)/(1-x)^3.
a(n) = Sum_{k=0..n-1} 10*k+1. [From Klaus Brockhaus, Nov 20 2008]
a(n) = 10*n+a(n-1)-9 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
a(n) = A131242(10n). - Philippe Deléham, Mar 27 2013
a(10*a(n)+46*n+1) = a(10*a(n)+46*n) + a(10*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[n-1]-a[n-2]+10 od: seq(a[n], n=0..42); - Zerinvary Lajos, Feb 18 2008
|
|
|
MATHEMATICA
|
s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 10}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 15 2008]
|
|
|
PROG
|
(MAGMA) [ n eq 1 select 0 else Self(n-1)+10*(n-2)+1: n in [1..43] ]; [From Klaus Brockhaus, Nov 20 2008]
(PARI) a(n)=(5*n-4)*n \\ Charles R Greathouse IV, Jun 16 2011
|
|
|
CROSSREFS
|
First differences of A007587.
Cf. A093645 ((10, 1) Pascal, column m=2). Partial sums of A017281.
Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, this sequence, A051865-A051876.
Sequence in context: A079561 A131543 A063296 * A039338 A118337 A032604
Adjacent sequences: A051621 A051622 A051623 * A051625 A051626 A051627
|
|
|
KEYWORD
|
easy,nonn,changed
|
|
|
AUTHOR
|
Barry E. Williams
|
|
|
EXTENSIONS
|
More terms from James A. Sellers, Dec 09 1999
|
|
|
STATUS
|
approved
|
| |
|
|
