A083880 a(0)=1, a(1)=5, a(n) = 10*a(n-1) - 23*a(n-2), n >= 2.

1, 5, 27, 155, 929, 5725, 35883, 227155, 1446241, 9237845, 59114907, 378678635, 2427143489, 15561826285, 99793962603, 640017621475, 4104915074881, 26328745454885, 168874407826587, 1083182932803515, 6947717948023649

Offset: 0

Author

Paul Barry, May 08 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083879.

Inverse binomial transform of A147957. 5th binomial transform of A077957. - Philippe Deléham, Nov 30 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-23).

Crossrefs

Cf. A083878, A006012.

Programs

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

Mathematica

LinearRecurrence[{10,-23},{1,5},30] (* Harvey P. Dale, May 14 2018 *)

PARI

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

Formula

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

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

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

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

a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2k)*2^(n-k))/5^n. - Philippe Deléham, Nov 30 2008

Extensions

Typo in definition corrected by Klaus Brockhaus, Dec 16 2008