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A004188 a(n) = n*(3*n^2 - 1)/2. 24
0, 1, 11, 39, 94, 185, 321, 511, 764, 1089, 1495, 1991, 2586, 3289, 4109, 5055, 6136, 7361, 8739, 10279, 11990, 13881, 15961, 18239, 20724, 23425, 26351, 29511, 32914, 36569, 40485, 44671, 49136, 53889, 58939, 64295, 69966, 75961 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

3-dimensional analog of centered polygonal numbers.

(1), (4+7), (10+13+16), (19+22+25+28), ... - Jon Perry, Sep 10 2004

REFERENCES

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140.

T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

Partial sums of n-1 3-spaced triangular numbers, e.g., a(4) = t(1) + t(4) + t(7) = 1 + 10 + 28 = 39. - Jon Perry, Jul 23 2003

a(n) = C(2*n+1,3) + C(n+1,3), n >= 0. - Zerinvary Lajos, Jan 21 2007

a(n) = A000447(n) + A000292(n). - Zerinvary Lajos, Jan 21 2007

G.f.: x*(1+7*x+x^2) / (x-1)^4. - R. J. Mathar, Oct 08 2011

From Miquel Cerda, Dec 25 2016: (Start)

a(n) = A000578(n) + A135503(n).

a(n) = A007588(n) - A135503(n). (End)

E.g.f.: (x/2)*(2 + 9*x + 3*x^2)*exp(x). - G. C. Greubel, Sep 01 2017

MAPLE

seq(binomial(2*n+1, 3)+binomial(n+1, 3), n=0..37); # Zerinvary Lajos, Jan 21 2007

MATHEMATICA

Table[n(3n^2-1)/2, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)

PROG

(PARI) vector(40, n, n*(3*n^2-1)/2)

(MAGMA) [n*(3*n^2-1)/2: n in [0..50]]; //Vincenzo Librandi, May 15 2011

CROSSREFS

1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.

Cf. A002412, A016061, A051682.

Cf. A236770 (partial sums).

Sequence in context: A103738 A045801 A162261 * A163634 A173373 A127867

Adjacent sequences:  A004185 A004186 A004187 * A004189 A004190 A004191

KEYWORD

nonn,easy

AUTHOR

Albert D. Rich (Albert_Rich(AT)msn.com)

STATUS

approved

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Last modified October 16 12:00 EDT 2018. Contains 316263 sequences. (Running on oeis4.)