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

Author

Roger L. Bagula and Gary W. Adamson, Sep 23 2006

Keywords

• nonn
• easy

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

Sequences of the form (m*i)^(n-2)*ChebyshevU(n-2, -i/m): A131577 (m=0), A000129 (m=1), A085449 (m=2), A002534 (m=3), A161007 (m=4), this sequence (m=5), A123005 (m=7), A123006 (m=11).

Programs

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

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