A131055 1 followed by repeats of 2*k.

1, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68, 68, 70, 70, 72

Offset: 1

Author

Gary W. Adamson, Jun 12 2007

Keywords

• nonn
• easy

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A131056.

Programs

Maple

seq(`if`(n=1, 1, n-(n mod 2)), n=1..72);

Mathematica

Join[{1}, Table[2*Floor[i/2], {i, 2, 81}]] (* Stefan Steinerberger, Jun 13 2007 *)
With[{c=2*Range[40]},Join[{1},Riffle[c,c]]] (* Harvey P. Dale, Jul 25 2019 *)

Formula

Inverse binomial transform of A131056: (1, 3, 7, 17, 41, 97, 225, ...).

From Colin Barker, Oct 28 2012: (Start)

a(n) = ((-1)^n + 2*n-1)/2 for n > 1.

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 1.

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

E.g.f.: x*(exp(x) + 1) - sinh(x). - Stefano Spezia, Jan 28 2024

Extensions

More terms from Stefan Steinerberger, Jun 13 2007