cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A239577 Expansion of 1/((x-1)*(3*x-1)*(3*x^2+1)).

Original entry on oeis.org

1, 4, 10, 28, 91, 280, 820, 2440, 7381, 22204, 66430, 199108, 597871, 1794160, 5380840, 16140880, 48427561, 145287604, 435848050, 1307529388, 3922632451, 11767941640, 35303692060, 105910943320, 317733228541, 953200084204, 2859599056870, 8578795974868
Offset: 0

Views

Author

Philippe Deléham, Mar 21 2014

Keywords

Examples

			Ternary................Decimal
1............................1
11...........................4
101.........................10
1001........................28
10101.......................91
101101.....................280
1010101....................820
10100101..................2440
101010101.................7381
1010110101...............22204
10101010101..............66430
101010010101............199108, etc.
		

Crossrefs

Programs

  • Mathematica
    Table[(-1 + 3^(2 + n) + (-1 + (-1)^n) (-3)^((1 + n)/2))/8, {n, 0, 30}] (* Bruno Berselli, Mar 24 2014 *)
    CoefficientList[Series[1/((x - 1) (3 x - 1) (3 x^2 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *)
    LinearRecurrence[{4,-6,12,-9},{1,4,10,28},30] (* Harvey P. Dale, Oct 04 2024 *)

Formula

G.f.: 1/((x-1)*(3*x-1)*(3*x^2+1)).
a(n) = Sum{k=0..n} A154957(n,k)*3^k.
a(n) = 4*a(n-1) - 6*a(n-2) + 12*a(n-3) - 9*a(n-4) for n > 3, a(0)=1, a(1)=4, a(2)=10, a(3)=16.
a(2*n) = A002452(n+1); a(2*n+1) = 4*A015251(n+2).
a(n) = ( -1 + 3^(2+n) + (-1+(-1)^n)*(-3)^((1+n)/2) )/8. [Bruno Berselli, Mar 24 2014]