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A064225 (9*n^2+5*n+2)/2. 8

%I

%S 1,8,24,49,83,126,178,239,309,388,476,573,679,794,918,1051,1193,1344,

%T 1504,1673,1851,2038,2234,2439,2653,2876,3108,3349,3599,3858,4126,

%U 4403,4689,4984,5288,5601,5923,6254,6594,6943,7301,7668,8044,8429,8823,9226

%N (9*n^2+5*n+2)/2.

%C Diagonal of triangular spiral in A051682. - _Michael Somos_, Jul 22 2006

%C Ehrhart polynomial of closed quadrilateral with vertices (0,2),(2,3),(3,1),(2,0). - _Michael Somos_, Jul 22 2006

%C In the natural number array A000027 this sequence is the first knight moves diagonal (A081267 is the second, A001844 is the main diagonal). It can be used to define this diagonal for any array: A007318(A064225-1)=A005809 (Subtraction by 1 because A007318 is defined with offset 0.) - _Tilman Piesk_, Mar 24 2012

%C Or positions of pentagonal numbers, such that p(a(n)) = p(a(n)-1) + p(3*n+1), where p=A000326. - _Vladimir Shevelev_, Jan 21 2014

%H Harry J. Smith, <a href="/A064225/b064225.txt">Table of n, a(n) for n = 0..1000</a>

%H National Security Agency, <a href="http://www.ams.org/notices/200202/rev-dauben.pdf">Intrigued? (advertisement)</a>, Notices of the Amer. Math. Soc., vol. 49 (2002), p. 216.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).

%F a(n) = 9*n+a(n-1)-2, with n>0, a(0) = 1. - _Vincenzo Librandi_, Aug 07 2010

%F a(0)=1, a(1)=8, a(2)=24, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Sep 13 2011

%F G.f.: (1+5*x+3*x^2)/(1-x)^3. - _Colin Barker_, Feb 23 2012

%F A064226(n) = a(-1-n). - _Michael Somos_, Jul 22 2006 (While the sequence itself is only one-way infinite, this identity works, as the defining formula (in the Name-field) produces integers also for the negative values of n, -1, -2, -3, etc.) - _Antti Karttunen_, Mar 24 2012

%t Table[(9n^2+5n+2)/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,8,24},51] (* _Harvey P. Dale_, Sep 13 2011 *)

%o (PARI) {a(n) = 1 + n * (9*n + 5) / 2}; /* _Michael Somos_, Jul 22 2006 */

%o (PARI) for (n=0, 1000, write("b064225.txt", n, " ", 1 + n*(9*n + 5)/2) ) \\ _Harry J. Smith_, Sep 10 2009

%o (Scheme) (define (A064225 n) (/ (+ (* 9 n n) (* 5 n) 2) 2))

%Y Cf. A064226, A081267, A235332.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Sep 22 2001

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)