A152767 3 times 10-gonal (or decagonal) numbers: 3n(4n-3).

0, 3, 30, 81, 156, 255, 378, 525, 696, 891, 1110, 1353, 1620, 1911, 2226, 2565, 2928, 3315, 3726, 4161, 4620, 5103, 5610, 6141, 6696, 7275, 7878, 8505, 9156, 9831, 10530, 11253, 12000, 12771, 13566, 14385, 15228, 16095, 16986

Offset

0,2

Comments

3*A172078(n) = n*a(n) - sum(a(k), k=0..n-1). - Bruno Berselli, Dec 12 2010

References

"Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Jan. 1910 p. 47 (Problem 1052).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 12*n^2 - 9*n = 3*A001107(n).

a(n) = a(n-1)+24*n-21, n>0. - Vincenzo Librandi, Nov 26 2010

a(n) = sum(A001539(k), k=0..n-1)-sum(4*A002939(k), k=0..n-1) if n>0 (see References, Problem 1052). - Bruno Berselli, Dec 08 2010 - Jan 21 2011

G.f.: -3*x*(1+7*x)/(x-1)^3.

a(0)=0, a(1)=3, a(2)=30, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, May 26 2012

Example

For n=8, a(8)=(1*3+5*7+9*11+..+29*31)-(2*4+6*8+10*12+..+26*28) = 696 (see Problem 1052 in References). - Bruno Berselli, Dec 12 2010

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 6!, 24}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 )
Table[3n(4n-3), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 3, 30}, 40] (* Harvey P. Dale, May 26 2012 *)

Prog

(PARI) a(n)=3*n*(4*n-3) \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

Cf. A001107, A139271.

3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A153783, A153448, A153875.

Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=24: see Comments lines of A226492.

Sequence in context: A208880 A012009 A001800 * A195029 A211617 A180816

Adjacent sequences: A152764 A152765 A152766 * A152768 A152769 A152770

Keyword

nonn,easy

Author

Omar E. Pol, Dec 15 2008

Status

approved