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 A064226 a(n) = (9*n^2 + 13*n + 6) / 2. 7
 3, 14, 34, 63, 101, 148, 204, 269, 343, 426, 518, 619, 729, 848, 976, 1113, 1259, 1414, 1578, 1751, 1933, 2124, 2324, 2533, 2751, 2978, 3214, 3459, 3713, 3976, 4248, 4529, 4819, 5118, 5426, 5743, 6069, 6404, 6748, 7101, 7463, 7834, 8214, 8603, 9001, 9408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Diagonal of triangular spiral in A051682. - Paul Barry, Mar 15 2003 Ehrhart polynomial of open quadrilateral with vertices (0,2),(2,3),(3,1),(2,0). - Michael Somos, Jul 22 2006 LINKS Harry J. Smith, Table of n, a(n) for n = 0..1000 Milan Janjic, Two Enumerative Functions 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) = 3*C(n, 0)+11*C(n, 1)+9*C(n, 2); binomial transform of (3, 11, 9, 0, 0, 0, .....). G.f.:(3+5*x+x^2)/(1-x)^3. - Paul Barry, Mar 15 2003 A064225(n) = a(-1-n). -  Michael Somos, Jul 22 2006 MAPLE A064226:=n-> (9*n^2 + 13*n + 6) / 2; seq(A064226(n), n=0..50); # Wesley Ivan Hurt, May 08 2014 MATHEMATICA Table[(9 n^2 + 13 n + 6)/2, {n, 0, 50}] (* Wesley Ivan Hurt, May 08 2014 *) LinearRecurrence[{3, -3, 1}, {3, 14, 34}, 50] (* Vincenzo Librandi, Jul 19 2015 *) PROG (PARI) {a(n) = 3 + n * (9*n + 13) / 2}; /* Michael Somos, Jul 22 2006 */ (PARI) for (n=0, 1000, write("b064226.txt", n, " ", 3 + n*(9*n + 13)/2) ) \\ Harry J. Smith, Sep 10 2009 (MAGMA) I:=[3, 14, 34]; [n le 3 select I[n] else 3*Self(n-1) - 3*Self(n-2) + Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 19 2015 CROSSREFS a(n) = A081268(n)+2. Cf. A051682, A081267. Cf. A064225. Cf. A235332. Sequence in context: A155154 A081269 A140064 * A077288 A094627 A009394 Adjacent sequences:  A064223 A064224 A064225 * A064227 A064228 A064229 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Sep 22 2001 STATUS approved

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