A160250 a(n) = 64*n^3 - 168*n^2 + 148*n - 43.

1, 93, 617, 1957, 4497, 8621, 14713, 23157, 34337, 48637, 66441, 88133, 114097, 144717, 180377, 221461, 268353, 321437, 381097, 447717, 521681, 603373, 693177, 791477, 898657, 1015101, 1141193, 1277317, 1423857, 1581197, 1749721, 1929813, 2121857, 2326237, 2543337, 2773541, 3017233

Offset

1,2

References

John H. Conway and Richard K. Guy, 'The Book of Numbers', Copernicus Pub. Co., 1996

Peter Pearce and Susan Pearce, 'Polyhedra primer', Van Nostrand Reinhold, 1978

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(1 + 89*x + 251*x^2 + 43*x^3)/(1-x)^4. - R. J. Mathar, Nov 10 2011

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jul 01 2012

E.g.f.: 43 + (-43 + 44*x + 24*x^2 + 64*x^3)*exp(x). - G. C. Greubel, Nov 14 2019

Maple

seq(((8*n-7)^3 +(8*n-1))/8, n=1..40); # G. C. Greubel, Nov 14 2019

Mathematica

CoefficientList[Series[(1+89*x+251*x^2+43*x^3)/(x-1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 01 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 93, 617, 1957}, 30] (* Harvey P. Dale, Mar 16 2013 *)
Table[((8*n-7)^3 +(8*n-1))/8, {n, 40}] (* G. C. Greubel, Nov 14 2019 *)

Prog

(Magma) I:=[1, 93, 617, 1957]; [n le 4 select I[n] else 4*Self(n-1) - 6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 01 2012
(PARI) a(n)=64*n^3-168*n^2+148*n-43 \\ Charles R Greathouse IV, Apr 25 2016
(Sage) [((8*n-7)^3 +(8*n-1))/8 for n in (1..40)] # G. C. Greubel, Nov 14 2019
(GAP) List([1..40], n-> ((8*n-7)^3 +(8*n-1))/8); # G. C. Greubel, Nov 14 2019

Crossrefs

Sequence in context: A146090 A160174 A238693 * A332614 A264556 A250373

Adjacent sequences: A160247 A160248 A160249 * A160251 A160252 A160253

Keyword

easy,nonn

Author

Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 05 2009, May 11 2009, May 19 2009

Extensions

Edited by G. C. Greubel, Nov 14 2019

Status

approved