A180844 - OEIS

%I #15 Jun 30 2023 16:28:55

%S 0,1,29,787,21257,573955,15496817,418414123,11297181449,305023899379,

%T 8235645283745,222362422662139,6003785411879801,162102206120758723,

%U 4376759565260493713,118172508262033346635,3190657723074900391913

%N a(n) = (27^n - 2^n)/25.

%C The a(n+1) appear in several triangle sums of Nicomachus's table A036561, i.e., Ca2(3*n), Ca2(3*n+1)/3, Ca2(3*n+2)/9 and Ca3(n). See A180662 for information about these camel sums and other chess sums.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (29, -54).

%F a(n) = (27^n - 2^n)/25.

%F G.f.: x/((27*x-1)*(2*x-1)).

%t (#[[1]]-#[[2]])/25&/@Partition[Riffle[27^Range[0,20],2^Range[0,20]],2]  (* _Harvey P. Dale_, Jan 22 2011 *)

%o (PARI) a(n) = (27^n - 2^n)/25 \\ _Iain Fox_, Dec 12 2017

%o (PARI) first(n) = Vec(x/((27*x-1)*(2*x-1)) + O(x^n), -n) \\ _Iain Fox_, Dec 12 2017

%Y Cf. A016153, A016140, A180844, A180845, A180846, A180847, A016185.

%K easy,nonn

%O 0,3

%A _Johannes W. Meijer_, Sep 21 2010