A122996 Expansion of (1+6*x)/(1-x-49*x^2).

1, 7, 56, 399, 3143, 22694, 176701, 1288707, 9947056, 73093699, 560499443, 4142090694, 31606563401, 234569007407, 1783290614056, 13277171976999, 100658412065743, 751239838938694, 5683502030160101, 42494254138156107

Offset: 0

Author

Roger L. Bagula, Sep 22 2006

Keywords

• nonn
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (1,49)

Crossrefs

Cf. A122995.

Programs

Magma

[n le 2 select 7^(n-1) else Self(n-1) + 49*Self(n-2): n in [1..41]]; // G. C. Greubel, Dec 23 2021

Mathematica

M:= {{0, 1}, {1, 1/7}}; v[1] = {1,1}; v[n_]:= v[n]= M.v[n-1];
Table[v[n][[1]]*7^(n-1), {n,30}]
LinearRecurrence[{1,49}, {1,7}, 40] (* G. C. Greubel, Dec 23 2021 *)

PARI

Vec((1+6*x)/(1-x-49*x^2) + O(x^30)) \\ Michel Marcus, Jan 28 2015

Sage

[(7*i)^n*( chebyshev_U(n, -i/14) - (6*i/7)*chebyshev_U(n-1, -i/14) ) for n in (0..40)] # G. C. Greubel, Dec 23 2021

Formula

a(n) = a(n-1) + 49*a(n-2). - Philippe Deléham, Mar 26 2009

a(n) = (1/2 + 13*sqrt(197)/394)*(1/2 + sqrt(197)/2)^n + (1/2 - 13*sqrt(197)/394)*(1/2 - sqrt(197)/2)^n. - Antonio Alberto Olivares, Jun 06 2011

a(n) = (7*i)^n*( ChebyshevU(n, -i/14) - (6*i/7)*ChebyshevU(n-1, -i/14) ). - G. C. Greubel, Dec 23 2021

Extensions

Edited by the Associate Editors of the OEIS, Sep 09 2009