This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056587 #34 Jul 01 2025 08:22:57
%S A056587 0,1,1,1024,59049,9765625,1073741824,137858491849,16679880978201,
%T A056587 2064377754059776,253295162119140625,31181719929966183601,
%U A056587 3833759992447475122176,471584161164422542970449
%N A056587 Tenth power of Fibonacci numbers A000045.
%C A056587 Divisibility sequence; that is, if n divides m, then a(n) divides a(m).
%D A056587 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 1, p. 85, (exercise 1.2.8. Nr. 30) and p. 492 (solution).
%H A056587 Vincenzo Librandi, <a href="/A056587/b056587.txt">Table of n, a(n) for n = 0..96</a>
%H A056587 A. Brousseau, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/6-1/brousseau3.pdf">A sequence of power formulas</a>, Fib. Quart., 6 (1968), 81-83.
%H A056587 J. Riordan, <a href="http://dx.doi.org/10.1215/S0012-7094-62-02902-2">Generating functions for powers of Fibonacci numbers</a>, Duke. Math. J. 29 (1962) 5-12.
%H A056587 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A056587 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (89,4895,-83215,-582505,1514513,1514513,-582505,-83215,4895,89,-1).
%F A056587 a(n) = F(n)^10, F(n)=A000045(n).
%F A056587 G.f.: x*p(10, x)/q(10, x) with p(10, x) := sum_{m=0..9} A056588(9, m)*x^m = (1-x)*(1 - 87*x - 4047*x^2 + 42186*x^3 + 205690*x^4 + 42186*x^5 - 4047*x^6 - 87*x^7 + x^8) and q(10, x) := sum_{m=0..11} A055870(11, m)*x^m = (1+x)*(1 - 3*x + x^2)*(1 + 7*x + x^2)*(1 - 18*x + x^2)*(1 + 47*x + x^2)*(1 - 123*x + x^2) (denominator factorization deduced from Riordan result).
%F A056587 Recursion (cf. Knuth's exercise): sum_{m=0..11} A055870(11, m)*a(n-m) = 0, n >= 11; inputs: a(n), n=0..10. a(n) = 89*a(n-1) + 4895*a(n-2) - 83215*a(n-3) - 582505*a(n-4) + 1514513*a(n-5) + 1514513*a(n-6) - 582505*a(n-7) -83215*a(n-8) + 4895*a(n-9) + 89*a(n-10) - a(n-11).
%t A056587 Fibonacci[Range[0,15]]^10 (* _Harvey P. Dale_, Jul 29 2018 *)
%o A056587 (Magma) [Fibonacci(n)^10: n in [0..20]]; // _Vincenzo Librandi_, Jun 04 2011
%o A056587 (PARI) a(n) = fibonacci(n)^10; \\ _Michel Marcus_, Sep 06 2017
%Y A056587 Cf. A000045, A007598, A056570, A056571, A056572, A056573, A056574, A056585, A056586, A056588, A055870.
%K A056587 nonn,easy
%O A056587 0,4
%A A056587 _Wolfdieter Lang_, Jul 10 2000
%E A056587 More terms from Larry Reeves (larryr(AT)acm.org), Jul 17 2001