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.
J. A. Siehler, Selections without adjacency on a rectangular grid, arXiv:1409.3869, Table 3, k=2 (different offset)
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
E.g.f.: exp(x)*(2 + 14*x + 9*x^2)/2. - Stefano Spezia, Dec 25 2022
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 22 2001
STATUS
approved