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A100747 A modular recurrence. 2
1, 3, 15, 45, 225, 675, 3375, 10125, 50625, 151875, 759375, 2278125, 11390625, 34171875, 170859375, 512578125, 2562890625, 7688671875, 38443359375, 115330078125, 576650390625, 1729951171875, 8649755859375, 25949267578125 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 16:32 EDT 2021. Contains 343742 sequences. (Running on oeis4.)