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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
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
MATHEMATICA
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 4, 7, 13, 18}, 100] (* Paolo Xausa, Feb 09 2024 *)
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. A085787. - R. J. Mathar, Aug 15 2008
Sequence in context: A310824 A266811 A085787 * A191138 A075315 A238327
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 March 19 07:04 EDT 2024. Contains 370953 sequences. (Running on oeis4.)