A122471 - OEIS

%I #17 Feb 26 2024 01:55:49

%S 1,6,40,277,1935,13540,94774,663411,4643869,32507074,227549508,

%T 1592846545,11149925803,78049480608,546346364242,3824424549679,

%U 26770971847737,187396802934142,1311777620538976,9182443343772813

%N a(n)=7*a(n-1)-n for n> 0, a(0)=1.

%C From a quiz.

%D K. Russell and P. Carter, Number Puzzles, W. Foulsham and Co. Ltd. (1993).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9, -15, 7).

%F G.f.: -(((x-3)*x+1)/((x-1)^2*(7*x-1))). - _Harvey P. Dale_, Jun 15 2011

%F a(0)=1, a(1)=6, a(2)=40, a(n)=9*a(n-1)-15*a(n-2)+7*a(n-3). - _Harvey P. Dale_, Jun 15 2011

%t RecurrenceTable[{a[0]==1,a[n]==7a[n-1]-n},a[n],{n,0,20}] (* or *) LinearRecurrence[{9,-15,7},{1,6,40},31](* _Harvey P. Dale_, Jun 15 2011 *)

%o (PARI) a(n)=if(n>0,7*a(n-1)-n,1) for(n=0,30,print1(a(n),","))

%K nonn

%O 0,2

%A Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 14 2006