login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A063523 n*(8*n^2-5)/3. 17
0, 1, 18, 67, 164, 325, 566, 903, 1352, 1929, 2650, 3531, 4588, 5837, 7294, 8975, 10896, 13073, 15522, 18259, 21300, 24661, 28358, 32407, 36824, 41625, 46826, 52443, 58492, 64989, 71950, 79391, 87328, 95777, 104754, 114275, 124356 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also as a(n)=(1/6)*(16*n^3-10*n), n>0: structured octagonal anti-diamond numbers (vertex structure 17) (Cf. A100187 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov 07 2004

REFERENCES

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

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,1000

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

FORMULA

a(0)=0, a(1)=1, a(2)=18, a(3)=67, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Jul 11 2011

G.f.: (x+14*x^2+x^3)/(x-1)^4. - _Harvey P. Dale, Jul 11 2011

MATHEMATICA

Table[n(8n^2-5)/3, {n, 0, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)

LinearRecurrence[{4, -6, 4, -1}, {0, 1, 18, 67}, 81] (* or *) CoefficientList[ Series[ (x+14 x^2+x^3)/(x-1)^4, {x, 0, 80}], x] (* Harvey P. Dale, Jul 11 2011 *)

PROG

(PARI) { for (n=0, 1000, write("b063523.txt", n, " ", n*(8*n^2 - 5)/3) ) } \\ Harry J. Smith, Aug 25 2009

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.

Sequence in context: A044156 A044537 A143859 * A045234 A158056 A214491

Adjacent sequences:  A063520 A063521 A063522 * A063524 A063525 A063526

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 02 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 00:38 EST 2016. Contains 278771 sequences.