A152767 3 times 10-gonal (or decagonal) numbers: a(n) = 3*n*(4*n-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, 17901, 18840, 19803, 20790, 21801

Offset: 0

Author

Omar E. Pol, Dec 15 2008

Keywords

• nonn
• easy

Comments

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

Examples

			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
		

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).

Crossrefs

Cf. A001107, A001539, A002939, A139271, A153794, A172078.

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.

Programs

Mathematica

Table[3n(4n-3),{n,0,40}] (* Harvey P. Dale, May 26 2012 *)

PARI

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

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_{k=0..n-1} A001539(k) - Sum_{k=0..n-1} 4*A002939(k) 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

From Elmo R. Oliveira, Dec 15 2024: (Start)

E.g.f.: 3*exp(x)*x*(1 + 4*x).

a(n) = A153794(n) - n. (End)