A025579 a(1)=1, a(2)=2, a(n) = 4*3^(n-3) for n >= 3.

1, 2, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395628, 172186884, 516560652, 1549681956, 4649045868, 13947137604, 41841412812, 125524238436, 376572715308, 1129718145924

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

a(n) is the sum of the numbers in row n+1 of the array defined in A025564 (and of the array in A024996).

a(n) is the number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2; |s(i) - s(i-1)| <= 1 for i >= 3.

Equals binomial transform of A095342: (1, 1, 5, 5, 17, 25, 61, ...). - Gary W. Adamson, Mar 04 2010

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3).

Crossrefs

Cf. A003946, A024996, A025564, A095342.

Programs

GAP

Concatenation([1,2], List([3..30], n-> 4*3^(n-3) )); # G. C. Greubel, Dec 26 2019

Magma

[1,2] cat [4*3^(n-3): n in [3..30]]; // G. C. Greubel, Dec 26 2019

Maple

seq( `if`(n<3, n, 4*3^(n-3)), n=1..30); # G. C. Greubel, Dec 26 2019

Mathematica

Join[{1,2},4*3^Range[0,30]] (* or *) Join[{1,2},NestList[3#&,4,30]] (* Harvey P. Dale, Jun 27 2011 *)

PARI

a(n)=max(n,4*3^(n-3)) \\ Charles R Greathouse IV, Jun 28 2011

PARI

Vec(x*(1+x)*(1-2*x)/(1-3*x) + O(x^30)) \\ Colin Barker, Oct 29 2019

Sage

[1,2]+[4*3^(n-3) for n in (3..30)] # G. C. Greubel, Dec 26 2019

Formula

a(n) = A003946(n-2), n>2. - R. J. Mathar, May 28 2008

From Colin Barker, Oct 29 2019: (Start)

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

a(n) = 3*a(n-1) for n>3. (End)

Extensions

Definition corrected by R. J. Mathar, May 28 2008