login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A153448 3 times 12-gonal (or dodecagonal) numbers: 3*n*(5*n-4). 12
0, 3, 36, 99, 192, 315, 468, 651, 864, 1107, 1380, 1683, 2016, 2379, 2772, 3195, 3648, 4131, 4644, 5187, 5760, 6363, 6996, 7659, 8352, 9075, 9828, 10611, 11424, 12267, 13140, 14043, 14976, 15939, 16932, 17955, 19008, 20091, 21204 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence is related to A172117 by 3*A172117(n) = n*a(n) - Sum_{i=0..n-1} a(i) and this is the case d=10 in the identity n*(3*n*(d*n - d + 2)/2) - Sum_{k=0..n-1} 3*k*(d*k - d + 2)/2 = n*(n+1)*(2*d*n - 2*d + 3)/2. - Bruno Berselli, Aug 26 2010

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 15*n^2 - 12*n = A051624(n)*3.

a(n) = 30*n + a(n-1) - 27 with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

G.f.: 3*x*(1 + 9*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=3, a(2)=36. - Harvey P. Dale, Jun 18 2014

E.g.f.: 3*x*(1 + 5*x)*exp(x). - G. C. Greubel, Aug 21 2016

a(n) = (4*n-2)^2 - (n-2)^2. In general, if P(k,n) is the k-th n-gonal number, then (2*k+1)*P(8*k+4,n) = ((3k+1)*n-2*k)^2 - (k*n-2*k))^2. - Charlie Marion, Jul 29 2021

MATHEMATICA

Table[3n(5n-4), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 3, 36}, 40] (* Harvey P. Dale, Jun 18 2014 *)

3*PolygonalNumber[12, Range[0, 60]] (* Harvey P. Dale, May 13 2022 *)

PROG

(PARI) a(n)=3*n*(5*n-4) \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A051624, A152965.

3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153783, A153875, A172117.

Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=30: see Comments lines of A226492.

Sequence in context: A072682 A158207 A227032 * A325838 A140958 A156189

Adjacent sequences: A153445 A153446 A153447 * A153449 A153450 A153451

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Dec 26 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 16:05 EST 2022. Contains 358701 sequences. (Running on oeis4.)