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A147837 a(n)=7*a(n-1)-5*a(n-2), a(0)=1, a(1)=5 . 2
1, 5, 30, 185, 1145, 7090, 43905, 271885, 1683670, 10426265, 64565505, 399827210, 2475962945, 15332604565, 94948417230, 587975897785, 3641089198345, 22547744899490, 139628768304705, 864662653635485, 5354494733924870 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

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

FORMULA

a(n)=Sum_{k, 0<=k<=n}A147703(n,k)*4^k. G.f.: (1-2x)/(1-7x+5*x^2).

a(n)=(1/2)*[(7/2)-(1/2)*sqrt(29)]^n-(3/58)*[(7/2)-(1/2)*sqrt(29)]^n*sqrt(29)+(3/58)*sqrt(29)*[(7/2)+(1 /2)*sqrt(29)]^n+1/2*[(7/2)+(1/2)*sqrt(29)]^n, with n>=0 [From Paolo P. Lava, Nov 18 2008]

a(n)= ((29+7*sqrt(29))/58)*(3.5+0.5*sqrt(29)^n +((29-7*sqrt(29))/58)*(3.5-0.5*sqrt(29)^n [From Richard Choulet, Nov 20 2008]

MATHEMATICA

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

CROSSREFS

Sequence in context: A136785 A227383 A155195 * A076036 A195257 A161407

Adjacent sequences:  A147834 A147835 A147836 * A147838 A147839 A147840

KEYWORD

nonn

AUTHOR

Philippe Deléham, Nov 14 2008

STATUS

approved

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Last modified February 22 23:14 EST 2020. Contains 332157 sequences. (Running on oeis4.)