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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

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