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

Author

Paul Curtz, Nov 24 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A168234.

Programs

Magma

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

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 *)

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)

Extensions

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