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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A106528 Values of y in x^2 - 289 = 2*y^2. 2
 6, 20, 34, 56, 126, 204, 330, 736, 1190, 1924, 4290, 6936, 11214, 25004, 40426, 65360, 145734, 235620, 380946, 849400, 1373294, 2220316, 4950666, 8004144, 12940950, 28854596, 46651570, 75425384, 168176910, 271905276, 439611354, 980206864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1). FORMULA a(3n) = 34*A001109(n). a(3n+1) = A001109(n+2) + 4*A001109(n+1) - 3*A001109(n) + 4*A001109(n-1). a(3n+2) = 4*A001109(n+2) - 3*A001109(n+1) + 4*A001109(n) + A001109(n-1). From Colin Barker, Mar 29 2012: (Start) a(n) = 6*a(n-3) - a(n-6). G.f.: 2*x*(3 +10*x +17*x^2 +10*x^3 +3*x^4)/(1 -6*x^3 +x^6). (End) EXAMPLE a(9) = 1190, 34*A001109(3) = 34*35 = 1190; a(10) = 1924, A001109(5) +4*A001109(4) -3*A001109(3) +4*A001109(2) = 1189 + 4*204 - 3*35 + 4*6 = 1924; a(11) =4290, 4*A001109(5) -3*A001109(4) +4*A001109(3) +A001109(2) = 4*1189 - 3*204 + 4*35 + 6 = 4290; also 2*4290^2 = A106527(11)^2 - 289 = 6067^2 - 289. MATHEMATICA LinearRecurrence[{0, 0, 6, 0, 0, -1}, {6, 20, 34, 56, 126, 204}, 40] (* G. C. Greubel, Aug 18 2021 *) PROG (MAGMA) I:=[6, 20, 34, 56, 126, 204]; [n le 6 select I[n] else 6*Self(n-3) - Self(n-6): n in [1..41]]; // G. C. Greubel, Aug 18 2021 (Sage) def A106528_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( 2*x*(3 +10*x +17*x^2 +10*x^3 +3*x^4)/(1 -6*x^3 +x^6) ).list() a=A106528_list(41); a[1:] # G. C. Greubel, Aug 18 2021 CROSSREFS Cf. A001109, A106527. Sequence in context: A226363 A253906 A031005 * A031068 A031052 A097811 Adjacent sequences:  A106525 A106526 A106527 * A106529 A106530 A106531 KEYWORD nonn AUTHOR Andras Erszegi (erszegi.andras(AT)chello.hu), May 09 2005 STATUS approved

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

Last modified January 22 10:13 EST 2022. Contains 350481 sequences. (Running on oeis4.)