A123009 Expansion of x*(1 + 5*x)/(1 - 2*x - 49*x^2).

1, 7, 63, 469, 4025, 31031, 259287, 2039093, 16783249, 133482055, 1089343311, 8719307317, 70816436873, 568878932279, 4607763271335, 37090594224341, 299961588744097, 2417362294480903, 19532842437422559, 157516437304409365

Offset: 1

Author

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

Keywords

• nonn
• easy

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

Cf. A002534, A123005.

Programs

Magma

[n le 2 select 7^(n-1) else 2*Self(n-1) + 25*Self(n-2): n in [1..31]]; // G. C. Greubel, Jul 13 2021

Mathematica

M:= {{0, 7}, {7, 2}}; v[1]= {1, 1}; v[n_]:= v[n]= M.v[n-1];
Table[v[n][[1]], {n, 30}]

Sage

[(7*i)^(n-2)*(5*chebyshev_U(n-2, -i/7) + 7*i*chebyshev_U(n-1, -i/7)) for n in (1..30)] # G. C. Greubel, Jul 13 2021

Formula

From Colin Barker, Oct 19 2012: (Start)

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

G.f.: x*(1 +5*x)/(1 -2*x -49*x^2). (End)

a(n) = (7*i)^(n-2)*(5*ChebyshevU(n-2, -i/7) + 7*i*ChebyshevU(n-1, -i/7)). - G. C. Greubel, Jul 13 2021

Extensions

Sequence edited by Joerg Arndt and Colin Barker, Oct 19 2012