%I A015445
%S A015445 1,1,10,19,109,280,1261,3781,15130,49159,185329,627760,2295721,
%T A015445 7945561,28607050,100117099,357580549,1258634440,4476859381,
%U A015445 15804569341,56096303770,198337427839,703204161769,2488241012320
%N A015445 Generalized Fibonacci numbers: a(n) = a(n-1) + 9 a(n-2).
%F A015445 a(n)={[ (1+sqrt(37))/2 ]^(n+1) - [ (1-sqrt(37))/2 ]^(n+1)}/sqrt(37).
%F A015445 a(n)=sum{k=0..floor(n/2), binomial(n-k, k)9^k } - Paul Barry (pbarry(AT)wit.ie), 
               Jul 20 2004
%F A015445 a(n)=sum{k=0..n, binomial((n+k)/2, (n-k)/2)(1+(-1)^(n-k))3^(n-k)/2}; 
               - Paul Barry (pbarry(AT)wit.ie), Aug 28 2005
%F A015445 a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-9)^(n-k). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 26 2008]
%o A015445 (Other) sage: [lucas_number1(n,1,-9) for n in xrange(1, 25)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A015445 Cf. A015443, A015442.
%Y A015445 Sequence in context: A131495 A060630 A070199 this_sequence A123001 A073222 
               A110463
%Y A015445 Adjacent sequences: A015442 A015443 A015444 this_sequence A015446 A015447 
               A015448
%K A015445 nonn,easy
%O A015445 0,3
%A A015445 Olivier Gerard (olivier.gerard(AT)gmail.com)