A083880 - OEIS

%I #19 Sep 08 2022 08:45:10

%S 1,5,27,155,929,5725,35883,227155,1446241,9237845,59114907,378678635,

%T 2427143489,15561826285,99793962603,640017621475,4104915074881,

%U 26328745454885,168874407826587,1083182932803515,6947717948023649

%N a(0)=1, a(1)=5, a(n) = 10*a(n-1) - 23*a(n-2), n >= 2.

%C Binomial transform of A083879.

%C Inverse binomial transform of A147957. 5th binomial transform of A077957. - _Philippe Deléham_, Nov 30 2008

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).

%F G.f.: (1-5x)/(1-10x+23x^2).

%F E.g.f.: exp(5x)cosh(x*sqrt(2)).

%F a(n) = ((5-sqrt(2))^n + (5+sqrt(2))^n)/2;

%F a(n) = Sum_{k=0..n} C(n, 2k)*5^(n-2k)*2^k.

%F a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2k)*2^(n-k))/5^n. - _Philippe Deléham_, Nov 30 2008

%t LinearRecurrence[{10,-23},{1,5},30] (* _Harvey P. Dale_, May 14 2018 *)

%o (PARI) a(n)=if(n<0,0,polsym(23-10*x+x^2,n)[n+1]/2)

%o (Magma) [ n eq 1 select 1 else n eq 2 select 5 else 10*Self(n-1)-23*Self(n-2): n in [1..21] ]; // _Klaus Brockhaus_, Dec 16 2008

%Y Cf. A083878, A006012.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 08 2003

%E Typo in definition corrected by _Klaus Brockhaus_, Dec 16 2008