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 A186349 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186348. 5
 1, 2, 4, 5, 8, 10, 13, 15, 19, 22, 26, 29, 34, 38, 43, 47, 53, 58, 64, 69, 76, 82, 89, 95, 103, 110, 118, 125, 134, 142, 151, 159, 169, 178, 188, 197, 208, 218, 229, 239, 251, 262, 274, 285, 298, 310, 323, 335, 349, 362, 376, 389, 404, 418, 433, 447, 463, 478, 494, 509, 526, 542, 559, 575, 593, 610, 628, 645, 664, 682, 701, 719, 739, 758, 778, 797, 818, 838, 859, 879, 901, 922, 944, 965, 988, 1010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) = n + floor((n^2 - 1)/8). a(n) = n + ceiling(n^2/8) - 1. - Wesley Ivan Hurt, Jun 28 2013 G.f.: x*(1 + x^2 - x^3 + x^4 - x^5)/((1+x)*(1+x^2)*(1-x)^3). - Bruno Berselli, Jul 05 2013 a(n) = (2*n*(n+8) - (1+(-1)^n)*(5+2*i^(n*(n+1))) - 2)/16 where i=sqrt(-1). - Bruno Berselli, Jul 05 2013 EXAMPLE First, write .....8...16..24..32..40..48..56..64..72..80.. (8i) 1..4..9..16...25...36.....49.....64.......81. (squares) Then replace each number by its rank, where ties are settled by ranking 8i after the square: p = (3,6,7,9,11,12,14,16,17,...) = A186348 = n + floor(sqrt(8n+1/2)). q = (1,2,4,5,8,10,13,15,19,...) = a(n). MAPLE seq(k+ceil(k^2/8)-1, k=1..100); # Wesley Ivan Hurt, Jun 28 2013 MATHEMATICA (* adjusted joint rank sequences p and q (=a(n)), using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2 + y*n + z *) d=-1/2; u=8; v=0; x=1; y=0; k[n_]:=(x*n^2+y*n-v+d)/u; a[n_]:=n+Floor[k[n]]; Table[a[n], {n, 1, 100}] PROG (MAGMA) m:=90; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x^2-x^3+x^4-x^5)/((1+x)*(1+x^2)*(1-x)^3))); // Bruno Berselli, Jul 05 2013 (PARI) a(n)=(n^2-1)\8+n \\ Charles R Greathouse IV, Jul 05 2013 (Maxima) makelist((2*n*(n+8)-(1+(-1)^n)*(5+2*%i^(n*(n+1)))-2)/16, n, 1, 90); /* Bruno Berselli, Jul 05 2013 */ CROSSREFS Cf. A186346, A186347, A186348. Sequence in context: A007729 A174868 A268381 * A304360 A072437 A115793 Adjacent sequences:  A186346 A186347 A186348 * A186350 A186351 A186352 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 20 2011 STATUS approved

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)