A171373 Binomial transform of A171372.

1, 6, 16, 36, 76, 152, 292, 552, 1052, 2052, 4104, 8344, 17044, 34664, 69904, 139808, 278108, 552268, 1098148, 2189908, 4379816, 8776356, 17596496, 35263836, 70598516, 141197032, 282208592, 563931612, 1127077552, 2253369432, 4506738864, 9015534644

Offset: 0

Author

Paul Curtz, Dec 07 2009

Keywords

• nonn

Comments

The recurrence shows that the sequence and its successive differences are identical to their fifth differences (see A135356).

Links

• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 2).

Programs

Mathematica

LinearRecurrence[{5,-10,10,-5,2},{1,6,16,36,76},40] (* Harvey P. Dale, Dec 09 2013 *)

Formula

a(n+1)-2*a(n) = 4*A105371(n-1) = 4*A138110(4,n).

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+2*a(n-5).

G.f.: (1+x-4*x^2+6*x^3+x^4)/((1-2*x)*(x^4-2*x^3+4*x^2-3*x+1)).

Extensions

Edited and extended by R. J. Mathar, Dec 15 2009, Mar 02 2010