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 A120871 a(n) is the value of j for row n of the fixed-j dispersion for Q = 8. 1
 1, 4, 2, 7, 8, 17, 7, 18, 17, 32, 14, 31, 9, 28, 23, 46, 16, 41, 34, 63, 25, 56, 14, 47, 36, 73, 23, 62, 49, 92, 34, 79, 64, 113, 47, 98, 28, 81, 62, 119, 41, 100, 79, 142, 56, 121, 31, 98, 73, 144, 46, 119, 92, 169, 63, 142, 113, 196, 82, 167, 49, 136, 103, 194 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence results from A087056 by deleting duplicates. LINKS Clark Kimberling, The equation (j+k+1)^2 - 4*k = Q*n^2 and related dispersions, Journal of Integer Sequences, 10 (2007), Article #07.2.7. EXAMPLE For each positive integer n, there is a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 8*n^2. This representation is used to define the fixed-j dispersion for Q = 8, given by A120860, having northwest corner:   1,  5,  29, 169, ...   2, 10,  58, 338, ...   3, 17,  99, 577, ...   4, 22, 128, 746, ...   ... The pair (j,k) for each n, shown in the position occupied by n in the above array, is shown here:   (1,2), (1,14),  (1,82),  (1,478), ...   (4,1), (4,25), (4,161),  (4,953), ...   (2,7), (2,47), (2,279), (2,1631), ...   (7,4), (7,56), (7,356), (7,2104), ...   ... The fixed-j for row 1 is a(1) = 1; the fixed-j for row 2 is a(2) = 4; etc. (For example, (4 + 25 + 1)^2 - 4*25 = 8*10^2.) PROG (PARI) f(n) = 3*n + 2*sqrtint(2*n^2); \\ A098021 unused(listus) = {my(v=vecsort(Vec(listus))); for (i=1, vecmax(v), if (!vecsearch(v, i), return (i)); ); }; D(nb) = {my(m = matrix(nb, nb), t); my(listus = List); for (g=1, nb, if (g==1, t = 1, t = unused(listus)); m[g, 1]=t; listput(listus, t); t = f(t); m[g, 2]=t; listput(listus, t); for (h=3, nb, t = 6*m[g, h-1] - m[g, h-2]; m[g, h] = t; listput(listus, t); ); ); m; }; \\ A120860 q(n) = 2*n^2 - sqrtint(2*n^2)^2; \\ A087056 lista(nn) = my(m=D(nn)); vector(nn, n, q(m[n, 1])); \\ Michel Marcus, Jul 09 2020 CROSSREFS Cf. A087056, A098021, A120860. Sequence in context: A128226 A049817 A203575 * A019689 A332651 A072009 Adjacent sequences:  A120868 A120869 A120870 * A120872 A120873 A120874 KEYWORD nonn AUTHOR Clark Kimberling, Jul 10 2006 EXTENSIONS More terms from Michel Marcus, Jul 09 2020 STATUS approved

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Last modified April 10 22:19 EDT 2021. Contains 342856 sequences. (Running on oeis4.)