A123005 Expansion of g.f. x^2/(1-2*x-49*x^2).

0, 1, 2, 53, 204, 3005, 16006, 179257, 1142808, 11069209, 78136010, 698663261, 5225991012, 44686481813, 345446523214, 2880530655265, 22687940948016, 186521884004017, 1484752874460818, 12109078065118469, 96971046978817020

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 (2,49).

Crossrefs

Sequences of the form (m*i)^(n-1)*ChebyshevU(n-1, -i/m): A131577 (m=0), A000129 (m=1), A085449 (m=2), A002534 (m=3), A161007 (m=4), A123004 (m=5), this sequence (m=7), A123006 (m=11).

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else 2*Self(n-1) -49*Self(n-2): n in [1..31]]; // G. C. Greubel, Jul 12 2021

Mathematica

CoefficientList[Series[x^2/(1-2x-49x^2),{x,0,30}],x] (* Harvey P. Dale, Apr 12 2020 *)

Sage

[(7*i)^(n-2)*chebyshev_U(n-2, -i/7) for n in [1..30]] # G. C. Greubel, Jul 12 2021

Formula

a(n) = 2*a(n-1) + 49*a(n-2).

a(n) = (7*i)^(n-2)*ChebyshevU(n-2, -i/7). - G. C. Greubel, Jul 12 2021

Extensions

Definition replaced by generating function - the Assoc. Eds. of the OEIS, Mar 27 2010