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
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
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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
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Maple
a:=n->mul(4+(-1)^j,j=1..n):seq(a(n),n=0..23); # Zerinvary Lajos, Dec 13 2008
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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 *) -
PARI
x='x+O('x^30); Vec((1+3*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) = (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
Comments