A081678 a(n) = (4*6^n - 3*5^n - 3^n)/6.

0, 1, 10, 77, 538, 3581, 23170, 147197, 923338, 5738621, 35418130, 217421117, 1329029338, 8096512061, 49190221090, 298195475837, 1804438818538, 10902948379901, 65799224576050, 396702889799357, 2389754663090938, 14386213437758141, 86555704435827010, 520526335200999677

Offset: 0

Author

Paul Barry, Mar 28 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081675.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (14,-63,90).

Crossrefs

Cf. A081675.

Programs

Magma

[(4*6^n-3*5^n-3^n)/6: n in [0..30]]; // Vincenzo Librandi, Jul 26 2011

Mathematica

Table[(4*6^n-3*5^n-3^n)/6,{n,0,20}] (* or *) LinearRecurrence[ {14,-63,90},{0,1,10},20] (* Harvey P. Dale, Jul 25 2011 *)

PARI

a(n)=(4*6^n-3*5^n-3^n)/6 \\ Charles R Greathouse IV, Jul 26 2011

Formula

G.f.: x*(1-4*x)/((1-3*x)*(1-5*x)*(1-6*x)).

a(n) = 14*a(n-1) - 63*a(n-2) + 90*a(n-3); a(0)=0, a(1)=1, a(2)=10. - Harvey P. Dale, Jul 25 2011

E.g.f.: exp(3*x)*(4*exp(3*x) - 3*exp(2*x) - 1)/6. - Elmo R. Oliveira, Sep 12 2024