This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050492 Thickened cube numbers: n*(n^2+(n-1)^2)+(n-1)*2*n*(n-1). 5
 1, 14, 63, 172, 365, 666, 1099, 1688, 2457, 3430, 4631, 6084, 7813, 9842, 12195, 14896, 17969, 21438, 25327, 29660, 34461, 39754, 45563, 51912, 58825, 66326, 74439, 83188, 92597, 102690, 113491, 125024, 137313, 150382, 164255, 178956 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In other words, positive integers n such that 2*n - 1 is a perfect cube. - Altug Alkan, Apr 15 2016 a(n) represents the first term in a sum of (2*n - 1)^3 consecutive integers which equals (2*n - 1)^6. - Patrick J. McNab, Dec 24 2016 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA a(n) = n*(4*n^2-6*n+3). a(1)=1, a(2)=14, a(3)=63, a(4)=172, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Oct 02 2011 G.f.: x*(1+10*x+13*x^2)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 04 2012 a(n) = ((2n-1)^3 + 1)/2. - Dave Durgin, May 07 2014 E.g.f.: x*(4*x^2 + 6*x + 1)*exp(x). - G. C. Greubel, Apr 15 2016 EXAMPLE ..... * * .. * .. * * a(2) = * .. * * .. * = 14 ..... * * .. * .. * * MATHEMATICA Table[n(n^2+(n-1)^2)+(n-1)2n(n-1), {n, 40}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 14, 63, 172}, 40] (* Harvey P. Dale, Oct 02 2011 *) PROG (MAGMA) [n*(4*n^2-6*n+3): n in [1..40]]; // Vincenzo Librandi, Oct 03 2011 (PARI) a(n)=n*(4*n^2-6*n+3) \\ Charles R Greathouse IV, Nov 10 2015 CROSSREFS Cf. A001844, A046092, A050533. Sequence in context: A022674 A044152 A044533 * A255499 A229739 A221909 Adjacent sequences:  A050489 A050490 A050491 * A050493 A050494 A050495 KEYWORD nonn,easy,nice AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)