login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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: A074136 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 16:11 EST 2018. Contains 299380 sequences. (Running on oeis4.)