A100747 A modular recurrence.

1, 3, 15, 45, 225, 675, 3375, 10125, 50625, 151875, 759375, 2278125, 11390625, 34171875, 170859375, 512578125, 2562890625, 7688671875, 38443359375, 115330078125, 576650390625, 1729951171875, 8649755859375, 25949267578125

Offset

0,2

Comments

Interpolated zeros suppressed.

The inverse mod 2 binomial transform of 2^n is 1,1,3,3,15,15,... (A100735).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,15).

Formula

a(n) = b(2*n) where b(0)=1, b(1)=0, b(n) = (5 - 2*(n/2 mod 2))b(n-2).

a(n) = A101553(2*(n+1))/5.

a(2*n) = 15^n, a(2*n+1) = 3 * 15^n. - Ralf Stephan, May 16 2007

O.g.f.: (1+3*x)/(1-15*x^2). - R. J. Mathar, Feb 04 2008

Maple

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

Mathematica

LinearRecurrence[{0, 15}, {1, 3}, 50] (* or *) RecurrenceTable[{a[n] == (5 - 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 *)

Prog

(PARI) x='x+O('x^30); Vec((1+3*x)/(1-15*x^2)) \\ G. C. Greubel, Apr 16 2018
(Magma) I:=[1, 3]; [n le 2 select I[n] else 15*Self(n-2): n in [1..30]]; // G. C. Greubel, Apr 16 2018

Crossrefs

Cf. A101553.

Bisection of A100735.

Sequence in context: A201868 A260021 A005560 * A100737 A178669 A110464

Adjacent sequences: A100744 A100745 A100746 * A100748 A100749 A100750

Keyword

easy,nonn

Author

Paul Barry, Dec 06 2004

Status

approved