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 A188313 A (25,-29) Somos-4 sequence. 4
 1, 3, 23, 314, 8209, 620297, 126742987, 47301104551, 32606721084786, 61958046554226593, 334806306946199122193, 3416372868727801226636179, 62595441409640805744780870839, 2993270782370572835241882188306602, 424202695773047673359251734568172738737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Hankel transform of A188312. LINKS G. C. Greubel, Table of n, a(n) for n = 0..74 FORMULA a(n) = (25*a(n-1)*a(n-3) - 29*a(n-2)^2)/a(n-4), n>=4. a(n) = b(-2*n) = b(2*n+3) = 2*b(n+2)^3*b(n+3) + b(n+1)^2*(b(n+3)*b(n+4) - b(n+2)*b(n+5)) for all n in Z where b(n) = A006720(n). - Michael Somos, Feb 28 2022 EXAMPLE G.f.: 1 + 3*x + 23*x^2 + 314*x^3 + 8209*x^4 + ... - Michael Somos, Feb 28 2022 MATHEMATICA Join[{1, 3, 23, 314}, RecurrenceTable[{a[n] == (25*a[n - 1]*a[n - 3] - 29*a[n - 2]^2)/a[n - 4], a[4] == 8209, a[5] == 620297, a[6] == 126742987, a[7] == 47301104551}, a, {n, 4, 25}]] (* G. C. Greubel, Aug 14 2018 *) b[ n_] := If[OddQ[n], a[(n-3)/2], a[-n/2]]; a[ n_] := If[-2<=n<=2, {2, 1, 1, 3, 23}[[n+3]], 2*b[n+2]^3*b[n+3] + b[n+1]^2*(b[n+3]*b[n+4] - b[n+2]*b[n+5])]; (* Michael Somos, Feb 28 2022 *) PROG (Magma) I:=[8209, 620297, 126742987, 47301104551]; [1, 3, 23, 314] cat [n le 4 select I[n] else (25*Self(n-1)*Self(n-3) - 29*Self(n-2)^2)/Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 14 2018 CROSSREFS Cf. A006720. Sequence in context: A231788 A356872 A088692 * A227821 A222076 A338301 Adjacent sequences: A188310 A188311 A188312 * A188314 A188315 A188316 KEYWORD nonn,easy AUTHOR Paul Barry, Mar 28 2011 STATUS approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)