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A136038 a(n) = n^6 - n^4. 1
0, 0, 48, 648, 3840, 15000, 45360, 115248, 258048, 524880, 990000, 1756920, 2965248, 4798248, 7491120, 11340000, 16711680, 24054048, 33907248, 46915560, 63840000, 85571640, 113145648, 147756048, 190771200, 243750000, 308458800, 386889048, 481275648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

From R. J. Mathar, Feb 06 2010: (Start)

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: 24*x^2*(1+x)*(2*x^2+11*x+2)/(1-x)^7. (End)

From Amiram Eldar, Jan 12 2021: (Start)

Sum_{n>=2} 1/a(n) = 11/4 - Pi^2/6 - Pi^4/90 = 11/4 - A013661 - A013662.

Sum_{n>=2} (-1)^n/a(n) = 7*Pi^4/720 + Pi^2/12 - 7/4 = A267315 + A072691 - 7/4. (End)

MAPLE

map(n -> n^6 - n^4, [$0..100]); # Robert Israel, Aug 28 2018

MATHEMATICA

a[n_]:=n^6-n^4; a[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011 *)

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 48, 648, 3840, 15000, 45360}, 30] (* Harvey P. Dale, May 17 2018 *)

PROG

(MAGMA) [n^6-n^4: n in [0..30]]; // Vincenzo Librandi, Feb 20 2012

CROSSREFS

Cf. A013661, A013662, A072691, A267315.

Sequence in context: A160286 A008658 A215893 * A233152 A138411 A186162

Adjacent sequences:  A136035 A136036 A136037 * A136039 A136040 A136041

KEYWORD

nonn,easy

AUTHOR

Rolf Pleisch, Mar 16 2008

STATUS

approved

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Last modified June 28 21:04 EDT 2022. Contains 354907 sequences. (Running on oeis4.)