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A064225 (9*n^2+5*n+2)/2. 8
1, 8, 24, 49, 83, 126, 178, 239, 309, 388, 476, 573, 679, 794, 918, 1051, 1193, 1344, 1504, 1673, 1851, 2038, 2234, 2439, 2653, 2876, 3108, 3349, 3599, 3858, 4126, 4403, 4689, 4984, 5288, 5601, 5923, 6254, 6594, 6943, 7301, 7668, 8044, 8429, 8823, 9226 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal of triangular spiral in A051682. - Michael Somos, Jul 22 2006

Ehrhart polynomial of closed quadrilateral with vertices (0,2),(2,3),(3,1),(2,0). - Michael Somos, Jul 22 2006

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

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

National Security Agency, Intrigued? (advertisement), Notices of the Amer. Math. Soc., vol. 49 (2002), p. 216.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

FORMULA

a(n) = 9*n+a(n-1)-2, with n>0, a(0) = 1. - Vincenzo Librandi, Aug 07 2010

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

G.f.: (1+5*x+3*x^2)/(1-x)^3. - Colin Barker, Feb 23 2012

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

MATHEMATICA

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

PROG

(PARI) {a(n) = 1 + n * (9*n + 5) / 2}; /* Michael Somos, Jul 22 2006 */

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

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

CROSSREFS

Cf. A064226, A081267, A235332.

Sequence in context: A146980 A028612 A068857 * A054275 A256857 A122655

Adjacent sequences:  A064222 A064223 A064224 * A064226 A064227 A064228

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 22 2001

STATUS

approved

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Last modified January 18 19:37 EST 2018. Contains 297865 sequences.