A152267 a(n) = ((9 + sqrt(8))^n + (9 - sqrt(8))^n)/2.

1, 9, 89, 945, 10513, 120249, 1397033, 16368417, 192648097, 2272771305, 26846572409, 317325998097, 3752068179889, 44372429376921, 524802751652681, 6207262185233025, 73420118463548737, 868431992821866441

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

Keywords

• nonn

Comments

Binomial transform of A145303. - Philippe Deléham, Dec 03 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (18, -73).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-8); S:=[ ((9+r8)^n+(9-r8)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008

Mathematica

LinearRecurrence[{18,-73},{1,9},30] (* Harvey P. Dale, May 14 2014 *)

Formula

From Philippe Deléham, Dec 03 2008: (Start)

a(n) = 18*a(n-1) - 73*a(n-2), n > 1; a(0)=1, a(1)=9.

G.f.: (1-9*x)/(1-18*x+73*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*8^(n-k). (End)

Extensions

Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008