A123004 Expansion of g.f. x^2/(1 - 2*x - 25*x^2).
0, 1, 2, 29, 108, 941, 4582, 32689, 179928, 1177081, 6852362, 43131749, 257572548, 1593438821, 9626191342, 59088353209, 358831489968, 2194871810161, 13360530869522, 81592856993069, 497198985724188, 3034219396275101
Offset: 1
References
- Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2, 25).
Crossrefs
Programs
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Magma
[n le 2 select n-1 else 2*Self(n-1) +25*Self(n-2): n in [1..30]]; // G. C. Greubel, Jul 12 2021
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Mathematica
Rest@CoefficientList[Series[x^2/(1 -2*x -25*x^2), {x,0,40}], x] Join[{a=0,b=1},Table[c=2*b+25*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *) -
Sage
[(5*i)^(n-2)*chebyshev_U(n-2, -i/5) for n in [1..30]] # G. C. Greubel, Jul 12 2021
Formula
a(n) = 2*a(n-1) + 25*a(n-2).
a(n+1) = ((1+sqrt(26))^n - (1-sqrt(26))^n)/(2*sqrt(26)). - Rolf Pleisch, Jul 06 2009
a(n) = (5*i)^(n-2)*ChebyshevU(n-2, -i/5). - G. C. Greubel, Jul 12 2021
Extensions
Definition replaced by generating function - the Assoc. Eds. of the OEIS, Mar 27 2010