|
| |
|
|
A069132
|
|
Centered 19-gonal numbers.
|
|
5
| |
|
|
1, 20, 58, 115, 191, 286, 400, 533, 685, 856, 1046, 1255, 1483, 1730, 1996, 2281, 2585, 2908, 3250, 3611, 3991, 4390, 4808, 5245, 5701, 6176, 6670, 7183, 7715, 8266, 8836, 9425, 10033, 10660, 11306, 11971, 12655, 13358, 14080, 14821, 15581, 16360, 17158
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Binomial transform of [1, 19, 19, 0, 0, 0,...] and Narayana transform (A001263) of [1, 19, 0, 0, 0,...]. - Gary W. Adamson, Jul 28 2011
|
|
|
LINKS
| E. Weisstein, Centered Polygonal Numbers
Index entries for sequences related to centered polygonal numbers
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1)
|
|
|
FORMULA
| a(n) = (19*n^2 - 19*n + 2)/2.
a(n) = 19*n+a(n-1)-19 (with a(1)=1) [From Vincenzo Librandi, Aug 08 2010]
G.f.: x*(1+17*x+x^2) / (1-x)^3 . - R. J. Mathar, Feb 04 2011
a(0)=1, a(1)=20, a(2)=58, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Aug 21 2011]
|
|
|
EXAMPLE
| a(5)= 191 because (19*5^2 - 19*5 + 2)/2 = (475 - 95 + 2)/2 = 382/2 = 191.
|
|
|
MATHEMATICA
| FoldList[#1 + #2 &, 1, 19 Range@ 45] (* Robert G. Wilson v, Feb 02 2011 *)
Table[(19n^2-19n+2)/2, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 20, 58}, 50] (* From Harvey P. Dale, Aug 21 2011 *)
|
|
|
PROG
| (PARI) a(n)=19*binomial(n, 2)+1 \\ Charles R Greathouse IV, Jul 29 2011
|
|
|
CROSSREFS
| Cf. A005448, A001844, A005891, A003215, A069099.
Sequence in context: A012483 A051872 A104100 * A124713 A126374 A163761
Adjacent sequences: A069129 A069130 A069131 * A069133 A069134 A069135
|
|
|
KEYWORD
| easy,nice,nonn
|
|
|
AUTHOR
| Terrel Trotter, Jr. (ttrotter(AT)telesal.net), Apr 07 2002
|
| |
|
|
