The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A033577 a(n) = (3*n+1) * (4*n+1). 9
 1, 20, 63, 130, 221, 336, 475, 638, 825, 1036, 1271, 1530, 1813, 2120, 2451, 2806, 3185, 3588, 4015, 4466, 4941, 5440, 5963, 6510, 7081, 7676, 8295, 8938, 9605, 10296, 11011, 11750, 12513, 13300, 14111, 14946, 15805, 16688, 17595, 18526, 19481, 20460, 21463 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the 120ยบ spoke (or ray) of a hexagonal spiral of Ulam. - Robert G. Wilson v, Jul 06 2014 If two independent real random variables x and y are distributed according to the same exponential distribution with pdf(x) = lambda * exp(-lambda * x) for some lambda > 0, then the probability that 3 <= x/(n*y) < 4 is given by n/a(n) for n>1. - Andres Cicuttin, Dec 11 2016 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Colin Barker, Dec 12 2016: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. G.f.: (1 + 17*x + 6*x^2)/(1-x)^3. (End) E.g.f.: (1 + 19*x + 12*x^2)*exp(x). - G. C. Greubel, Oct 12 2019 EXAMPLE See A056105 example section for hexagonal spiral of Ulam diagram. - Robert G. Wilson v, Jul 06 2014 MAPLE A033577:=n->(3*n+1)*(4*n+1): seq(A033577(n), n=0..50); # Wesley Ivan Hurt, Jul 06 2014 MATHEMATICA f[n_] := (3n + 1)(4n + 1); Array[f, 50, 0] (* Robert G. Wilson v, Jul 06 2014 *) LinearRecurrence[{3, -3, 1}, {1, 20, 63}, 50] (* Harvey P. Dale, Jul 16 2020 *) PROG (PARI) vector(50, m, 12*m^2 - 17*m + 6) \\ Michel Marcus, Jul 06 2014 (PARI) Vec((1 + 17*x + 6*x^2) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Dec 12 2016 (MAGMA) [(3*n+1)*(4*n+1) : n in [0..50]]; // Wesley Ivan Hurt, Jul 06 2014 (Sage) [(3*n+1)*(4*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019 (GAP) List([0..50], n-> (3*n+1)*(4*n+1)); # G. C. Greubel, Oct 12 2019 CROSSREFS Subsequence of A281333. Cf. A003215, A056105, A056106, A056107, A056108, A056109, A244802, A244803, A244804, A244805, A244806. Sequence in context: A117431 A159504 A117432 * A262486 A187156 A246877 Adjacent sequences:  A033574 A033575 A033576 * A033578 A033579 A033580 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Wesley Ivan Hurt, Jul 06 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 17 07:58 EST 2021. Contains 340214 sequences. (Running on oeis4.)