A141530 a(n) = 4*n^3 - 6*n^2 + 1.

1, -1, 9, 55, 161, 351, 649, 1079, 1665, 2431, 3401, 4599, 6049, 7775, 9801, 12151, 14849, 17919, 21385, 25271, 29601, 34399, 39689, 45495, 51841, 58751, 66249, 74359, 83105, 92511, 102601, 113399, 124929, 137215, 150281, 164151, 178849, 194399, 210825, 228151

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

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

Formula

a(n) = (2*n-1)*(2*n^2 - 2*n - 1) = A060747(n)*A132209(n-1), n > 1. - R. J. Mathar, Feb 22 2009

G.f.: (1 - 5*x + 19*x^2 + 9*x^3)/(1-x)^4. - Jaume Oliver Lafont, Aug 30 2009

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1, a(1)=-1, a(2)=9, a(3)=55. - Harvey P. Dale, Nov 30 2011

E.g.f.: (1 - 2*x + 6*x^2 + 4*x^3)*exp(x). - G. C. Greubel, Mar 29 2021

Maple

A141530:= n-> 4*n^3 -6*n^2 +1; seq(A141530(n), n=0..50); # G. C. Greubel, Mar 29 2021

Mathematica

Array[4*#^3-6*#^2+1&, 50, 0] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
LinearRecurrence[{4, -6, 4, -1}, {1, -1, 9, 55}, 50] (* Harvey P. Dale, Nov 30 2011 *)

Prog

(PARI) a(n)=4*n^3-6*n^2+1 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [4*n^3 -6*n^2 +1: n in [0..50]]; // G. C. Greubel, Mar 29 2021
(Sage) [4*n^3 -6*n^2 +1 for n in (0..50)] # G. C. Greubel, Mar 29 2021
(Python)
def A141530(n): return (m:=(n<<1)-1)*(n*(m-1)-1) # Chai Wah Wu, Mar 11 2024

Crossrefs

Cf. A046092, A141047, A141417.

See Librandi's comment in A078371.

Sequence in context: A145875 A299519 A068970 * A263478 A326249 A016269

Adjacent sequences: A141527 A141528 A141529 * A141531 A141532 A141533

Keyword

sign,less,easy

Author

Paul Curtz, Aug 12 2008

Extensions

Corrected, completed and edited, following an observation from Vincenzo Librandi, by M. F. Hasler, Feb 12 2009

Further edited by N. J. A. Sloane, Feb 13 2009

Status

approved