A147837 a(n)=7*a(n-1)-5*a(n-2), a(0)=1, a(1)=5.

1, 5, 30, 185, 1145, 7090, 43905, 271885, 1683670, 10426265, 64565505, 399827210, 2475962945, 15332604565, 94948417230, 587975897785, 3641089198345, 22547744899490, 139628768304705, 864662653635485, 5354494733924870, 33158149869296665, 205334575415452305

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (7,-5).

Formula

a(n) = Sum_{k=0..n} A147703(n,k)*4^k.

G.f.: (1-2*x)/(1-7*x+5*x^2).

a(n) = ((29+3*sqrt(29))/58)*(3.5+0.5*sqrt(29))^n +((29-3*sqrt(29))/58)*(3.5-0.5*sqrt(29))^n. - Richard Choulet, Nov 20 2008 [corrected by Jason Yuen, Oct 04 2024]

Mathematica

LinearRecurrence[{7, -5}, {1, 5}, 30] (* Harvey P. Dale, Oct 10 2015 *)

Crossrefs

Cf. A147703.

Sequence in context: A136785 A227383 A155195 * A076036 A195257 A161407

Adjacent sequences: A147834 A147835 A147836 * A147838 A147839 A147840

Keyword

nonn,easy

Author

Philippe Deléham, Nov 14 2008

Status

approved