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A027602 a(n) = n^3 + (n+1)^3 + (n+2)^3. 11
9, 36, 99, 216, 405, 684, 1071, 1584, 2241, 3060, 4059, 5256, 6669, 8316, 10215, 12384, 14841, 17604, 20691, 24120, 27909, 32076, 36639, 41616, 47025, 52884, 59211, 66024, 73341, 81180, 89559, 98496, 108009, 118116, 128835, 140184 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(3) = 216 = 6^3 (a cube). - Howard Berman (howard_berman(AT)hotmail.com), Nov 07 2008

Pairs [n,a(n)] for n<=10^7 such that a(n) is a perfect power are [0, 9], [1, 36], [3, 216], [23, 41616]. - Joerg Arndt, Jan 25 2011

Sums of three consecutive cubes. - Al Hakanson (hawkuu(AT)gmail.com), May 20 2009

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..750

P. De Geest, Palindromic Sums of Cubes of Consecutive Integers

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

FORMULA

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 1*a(n-4) for n>=4.

a(n) = 9*A006527(n+1). - Lekraj Beedassy, Feb 01 2007

a(n) = 3*n^3 + 9*n^2 + 15*n + 9.

G.f.: 9*(1+x^2)/(1-x)^4. - Bruno Berselli, Jan 21 2011

a(n) = A008585(n+1)*A059100(n+1). - Bruno Berselli, Jan 21 2011

MATHEMATICA

f[n_]:=n^3; Table[f[n]+f[n+1]+f[n+2], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 03 2009 *)

PROG

(Sage) [i^3+(i+1)^3+(i+2)^3 for i in xrange(0, 48)] # Zerinvary Lajos, Jul 03 2008

(MAGMA) [3*n^3 + 9*n^2 + 15*n + 9: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011

(PARI) a(n)=3*(n^3 + 3*n^2 + 5*n + 3) \\ Charles R Greathouse IV, Jun 11 2015

(Python)

A027602_list, m = [], [18, 0, 9, 9]

for _ in range(10**2):

    A027602_list.append(m[-1])

    for i in range(3):

        m[i+1] += m[i] # Chai Wah Wu, Dec 15 2015

CROSSREFS

Cf. A003215, A000537, A000578, A005898.

Sequence in context: A022604 A085630 A133226 * A231670 A134537 A066647

Adjacent sequences:  A027599 A027600 A027601 * A027603 A027604 A027605

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified August 21 02:25 EDT 2017. Contains 290855 sequences.