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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: A319576 A028612 A068857 * A304844 A054275 A256857 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 October 21 14:56 EDT 2019. Contains 328301 sequences. (Running on oeis4.)