A168388 First number in the n-th row of A172002.

1, 3, 5, 13, 21, 39, 57, 89, 121, 171, 221, 293, 365, 463, 561, 689, 817, 979, 1141, 1341, 1541, 1783, 2025, 2313, 2601, 2939, 3277, 3669, 4061, 4511, 4961, 5473, 5985, 6563, 7141, 7789, 8437, 9159, 9881, 10681, 11481, 12363, 13245, 14213, 15181, 16239, 17297

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, -1).

Formula

a(2*n+1) = A166464(n) a(2*n) = A166911(n).

a(n+1) - a(n) = A093907(n-1), n>1.

a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6).

G.f.: x*(1 - x^2 + 2*x)*(1 - x + x^2 + x^3)/( (1+x)^2 * (x-1)^4).

a(n+1) = A168380(n)+1.

From G. C. Greubel, Jul 19 2016: (Start)

a(n) = (12 + n + 3*(-1)^n*n + 2*n^3)/12.

E.g.f.: (1/12)*( -3*x - 12*exp(x) + (12 + 3*x + 6*x^2 + 2*x^3)*exp(2*x) )*exp(-x). (End)

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 3, 5, 13, 21, 39}, 50] (* Harvey P. Dale, Nov 29 2014 *)
Table[(n + 1) (3 + 2 n^2 + 4 n - 3 (-1)^n)/12 + 1, {n, 0, 46}] (* Michael De Vlieger, Jul 19 2016, after Vincenzo Librandi at A168380 *)

Prog

(Magma) [(12+n+3*(-1)^n*n+2*n^3)/12: n in [1..60]]; // Vincenzo Librandi, Jul 20 2016

Crossrefs

Cf. A168234.

Sequence in context: A222752 A172143 A218790 * A059872 A059873 A239314

Adjacent sequences: A168385 A168386 A168387 * A168389 A168390 A168391

Keyword

nonn,easy

Author

Paul Curtz, Nov 24 2009

Extensions

Edited and extended by R. J. Mathar, Mar 25 2010

Status

approved