The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006051 Square hex numbers. (Formerly M5409) 6
 1, 169, 32761, 6355441, 1232922769, 239180661721, 46399815451081, 9001325016847969, 1746210653453054881, 338755865444875798921, 65716891685652451935769, 12748738231151130799740241, 2473189499951633722697670961, 479786014252385791072548426169 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers n of the form n = y^2 = 3*x^2 - 3*x + 1. REFERENCES M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 19. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 1..435 M. Gardner & N. J. A. Sloane, Correspondence, 1973-74 Giovanni Lucca, Integer Sequences and Circle Chains Inside a Circular Segment, Forum Geometricorum, Vol. 18 (2018), 47-55. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Sociedad Magic Penny Patagonia, Leonardo en Patagonia Eric Weisstein's World of Mathematics, Hex Number. Index entries for linear recurrences with constant coefficients, signature (195,-195,1). FORMULA a(n) = A001570(n)^2. a(1 - n) = a(n). G.f.: x * (1 - 26*x + x^2) / ((1 - x) * (1 - 194*x + x^2)). - Simon Plouffe in his 1992 dissertation a(n) = 194*a(n-1) - a(n-2) - 24, a(1)=1, a(2)=169. - James A. Sellers, Jul 04 2000 a(n+1) = A003215(A001921(n)). - Joerg Arndt, Jan 02 2017 a(n) = (1/8)*(1 + 7*(ChebyshevU(n-1, 97) - ChebyshevU(n-2, 97))). - G. C. Greubel, Oct 07 2022 EXAMPLE G.f. = x + 169*x^2 + 32761*x^3 + 6355441*x^4 + 1232922769*x^5 + ... MATHEMATICA Rest@ CoefficientList[Series[x(1-26x+x^2)/((1-x)(1-194x+x^2)), {x, 0, 20}], x] (* Michael De Vlieger, Jan 02 2017 *) LinearRecurrence[{195, -195, 1}, {1, 169, 32761}, 20] (* Harvey P. Dale, Nov 03 2017 *) PROG (PARI) {a(n) = sqr( real( (2 + quadgen( 12)) ^ (2*n - 1)) / 2)} /* Michael Somos, Feb 15 2011 */ (Magma) [(7*Evaluate(ChebyshevSecond(n), 97) - 7*Evaluate(ChebyshevU(n-1), 97) + 1)/8: n in [1..30]]; // G. C. Greubel, Nov 04 2017; Oct 07 2022 (SageMath) def A006051(n): return (7*chebyshev_U(n-1, 97) - 7*chebyshev_U(n-2, 97) + 1)/8 [A006051(n) for n in range(1, 31)] # G. C. Greubel, Oct 07 2022 CROSSREFS Cf. A003500. Intersection of A000290 and A003215. Values of x are given by A001922, values of y by A001570. Sequence in context: A051477 A227692 A260862 * A069742 A069743 A210087 Adjacent sequences: A006048 A006049 A006050 * A006052 A006053 A006054 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 16 22:07 EDT 2024. Contains 371755 sequences. (Running on oeis4.)