A102877 a(0) = 1, a(1) = 1; for n>0, a(2*n) = 3*a(2n-1), a(2*n+1) = 3*a(2*n) - 2*a(n-1).

1, 1, 3, 7, 21, 61, 183, 543, 1629, 4873, 14619, 43815, 131445, 394213, 1182639, 3547551, 10642653, 31926873, 95780619, 287338599, 862015797, 2586037645, 7758112935, 23274309567, 69822928701, 209468698473, 628406095419

Offset

0,3

Comments

The sequence of first differences of these numbers (2, 4, 14, 40 ...), divided by 2, is (1, 2, 7, 20, ...) - see A111017. This is close to the original sequence.

..... 1, 1, 3, 7, 21, 61, 183, 543, 1629, 4873, 14619

........ 1, 2, 7, 20, 61, 180, 543, 1622, 4873, 14598

....... 2=3-1, 20=21-1, 180=183-3, 1622=1629-7, 14598=14619-21.

Links

Robert Israel, Table of n, a(n) for n = 0..2095

Formula

G.f. g(z) satisfies g(z) = 1 - 2*z + 3*z*g(z) - 2*z^3*g(z^2). - Robert Israel, Jun 29 2020

Maple

f:= proc(n) option remember; if n::even then 3*procname(n-1) else 3*procname(n-1)-2*procname((n-3)/2) fi end proc:
f(0):= 1: f(1):= 1:
map(f, [$0..50]); # Robert Israel, Jun 29 2020

Mathematica

a[0]:=1; a[1]:=1; a[n_]:=If[EvenQ[n], 3*a[n-1], 3*a[n-1]-2*a[(n-3)/2]]; Table[a[i], {i, 0, 50}] (* Stefan Steinerberger, May 22 2007 *)

Prog

(PARI) {m=26; v=vector(m+1); v[1]=1; v[2]=1; for(n=2, m, k=3*v[n]; if(n%2==1, k=k-2*v[(n-1)/2]); v[n+1]=k); print(v)} /* Klaus Brockhaus, May 20 2007 */

Crossrefs

This sequence is connected with A129770 and A129772.

Sequence in context: A091486 A056779 A183113 * A122983 A351822 A005355

Adjacent sequences: A102874 A102875 A102876 * A102878 A102879 A102880

Keyword

nonn

Author

Paul Curtz, May 16 2007

Extensions

More terms from Klaus Brockhaus and Stefan Steinerberger, May 20 2007

Status

approved