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 A111710 Consider the triangle shown below in which the n-th row contains the n smallest numbers greater than those in the previous row such that the arithmetic mean is an integer. Sequence contains the leading diagonal. 4
 1, 4, 7, 13, 18, 27, 34, 46, 55, 70, 81, 99, 112, 133, 148, 172, 189, 216, 235, 265, 286, 319, 342, 378, 403, 442, 469, 511, 540, 585, 616, 664, 697, 748, 783, 837, 874, 931, 970, 1030, 1071, 1134, 1177, 1243, 1288, 1357, 1404, 1476, 1525, 1600, 1651, 1729 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(1)=1, a(2n) = a(2n-1)+3n, a(2n+1)=a(2n)+2n+1. - Franklin T. Adams-Watters, May 01 2006 G.f. -x*(1+3*x+x^2) / ( (1+x)^2*(x-1)^3 ). a(n+1)-a(n) = A080512(n+1). - R. J. Mathar, May 02 2013 From Colin Barker, Jan 26 2016: (Start) a(n) = (10*n^2+2*(-1)^n*n+10*n+(-1)^n-1)/16. a(n) = (5*n^2+6*n)/8 for n even. a(n) = (5*n^2+4*n-1)/8 for n odd. (End) EXAMPLE The fourth row is 8,9,10 and 13,(8+9+10 +13)/4 = 10. Triangle begins: 1 2 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 21 22 23 27 28 29 30 31 32 33 34 PROG (PARI) Vec(x*(1+3*x+x^2)/((1-x)^3*(1+x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016 CROSSREFS Cf. A111711, A111712. Cf. A085787. - R. J. Mathar, Aug 15 2008 Sequence in context: A310824 A266811 A085787 * A191138 A075315 A238327 Adjacent sequences:  A111707 A111708 A111709 * A111711 A111712 A111713 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Aug 24 2005 EXTENSIONS More terms from Franklin T. Adams-Watters, May 01 2006 STATUS approved

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Last modified October 18 11:56 EDT 2018. Contains 316321 sequences. (Running on oeis4.)