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A281619 Integer values of (A000045^2-1)/9 where A000045(m) is the m-th Fibonacci number.

%I A281619 #25 Jan 05 2025 19:51:41
%S A281619 0,7,336,880,6032,15792,741895,34853280,91247072,625416736,1637362272,
%T A281619 76921173511,3613657792752,9460678925136,64844458022832,
%U A281619 169764995085840,7975341111241735,374671267233275712,980902112224710592,6723203096097857600,17601574218852716736,826899317018844410887
%N A281619 Integer values of (A000045^2-1)/9 where A000045(m) is the m-th Fibonacci number.
%C A281619 Also the integer values of A080097/9 where A080097(m) = Fibonacci(n+2)^2 - 1.
%C A281619 The indices of the Fibonacci numbers are 1, 2, 6, 10, and 11 mod 12. See the Wulczy link.
%H A281619 Robert Israel, <a href="/A281619/b281619.txt">Table of n, a(n) for n = 1..997</a>
%H A281619 G. Wulczy, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/13-1/advanced13-1.pdf">Unity with Fibonacci, Problem H-247 and solution</a>, Fib. Quarter. p. 89_90, Vol 15, 1, Feb. 1977.
%F A281619 G.f.: x^2*(7*x^10+336*x^9+880*x^8+6032*x^7+15792*x^6+16114*x^5+15792*x^4
%F A281619 +6032*x^3+880*x^2+336*x+7)/(-x^15+103683*x^10-103683*x^5+1). - _Robert Israel_, Mar 05 2017
%p A281619 seq(seq((combinat:-fibonacci(12*m+j)^2-1)/9,j=[2,6,10,11,13]),m=0..20); # _Robert Israel_, Mar 05 2017
%t A281619 Select[(#^2-1)/9&/@Fibonacci[Range[100]],IntegerQ] (* _Harvey P. Dale_, Feb 07 2017 *)
%o A281619 (PARI) lista(nn)=v = [1, 2, 6, 10, 11, 13, 14, 18, 22, 23]; for (n=1, nn, j = (n % #v) +1; k = n\#v; print1((fibonacci(24*k+v[j])^2-1)/9, ", "););
%o A281619 (PARI) a(n)=fibonacci(n\5*12+[1, 2, 6, 10, 11][n%5+1])^2\9 \\ _Charles R Greathouse IV_, Jan 26 2017
%Y A281619 Cf. A000045, A007887, A080097.
%K A281619 nonn,easy
%O A281619 1,2
%A A281619 _Michel Marcus_, Jan 25 2017