A081890 - OEIS

%I #17 Sep 12 2024 19:59:15

%S 1,3,7,33,643,11073,151867,1816713,19996963,208630833,2099398027,

%T 20597485593,198424412083,1885822419393,17740469253787,

%U 165580566245673,1535948935336003,14178113530908753,130361707324735147,1194785495130736953,10921581632007328723,99616564791408530913

%N a(n) = 9^n - 8^n - 7^n - 6^n + 3*5^n.

%C Binomial transform of A081687.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (35,-485,3325,-11274,15120).

%F G.f.: -(4182*x^4-2082*x^3+387*x^2-32*x+1)/((5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)). [_Colin Barker_, Aug 12 2012]

%F From _Elmo R. Oliveira_, Sep 12 2024: (Start)

%F E.g.f.: exp(5*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).

%F a(n) = 35*a(n-1) - 485*a(n-2) + 3325*a(n-3) - 11274*a(n-4) + 15120*a(n-5) for n > 4. (End)

%t LinearRecurrence[{35,-485,3325,-11274,15120},{1,3,7,33,643},30] (* _Harvey P. Dale_, Jun 26 2017 *)

%Y Cf. A081687, A081691.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 30 2003

%E a(19)-a(21) from _Elmo R. Oliveira_, Sep 12 2024