A101553 A modular recurrence.

1, 5, 15, 75, 225, 1125, 3375, 16875, 50625, 253125, 759375, 3796875, 11390625, 56953125, 170859375, 854296875, 2562890625, 12814453125, 38443359375, 192216796875, 576650390625, 2883251953125, 8649755859375, 43248779296875

Offset: 0

Author

Paul Barry, Dec 06 2004

Keywords

• easy
• nonn

Comments

Interpolated zeros suppressed.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,15).

Programs

Magma

I:=[1,5]; [n le 2 select I[n] else 15*Self(n-2): n in [1..30]]; // G. C. Greubel, Apr 16 2018

Maple

a:=n->mul(4-(-1)^j,j=1..n):seq(a(n),n=0..23); # Zerinvary Lajos, Dec 13 2008

Mathematica

CoefficientList[Series[(1+5x)/(1-15x^2),{x,0,30}],x] (* or *) LinearRecurrence[ {0,15},{1,5},30] (* Harvey P. Dale, Oct 14 2013 *)
RecurrenceTable[{a[n] == (3 + 2*Mod[n/2, 2])*a[n - 2], a[0] == 1, a[1] == 0}, a, {n, 0, 50}][[1 ;; ;; 2]] (* G. C. Greubel, Apr 16 2018 *)

PARI

x='x+O('x^30); Vec((1+5*x)/(1-15*x^2))  \\ G. C. Greubel, Apr 16 2018

Formula

a(n) = b(2*n) where b(0)=1, b(1)=0, b(n) = (3 + 2*(n/2 mod 2))*b(n-2).

a(n) = A100747(2(n+1))/3.

a(2n) = 15^n, a(2n+1) = 5*15^n. - Ralf Stephan, May 16 2007

O.g.f.: (1+5*x)/(1-15*x^2). - Philippe Deléham, Dec 02 2011