login
Numbers which are the sum of two positive triangular numbers in more than one way.
2

%I #11 May 09 2021 10:57:29

%S 16,31,42,46,51,56,72,76,81,94,106,111,121,123,126,133,141,146,156,

%T 157,172,174,181,186,191,196,198,211,216,225,226,231,237,241,246,256,

%U 259,268,276,281,286,289,291,297,301,306,310,315,321,326,328,331,336,342,346,354,361,366,367

%N Numbers which are the sum of two positive triangular numbers in more than one way.

%C This is a subsequence of A020756 (sums of two triangular numbers).

%C This is also a subsequence of A051533 (sums of two positive triangular numbers). This is not a subsequence of A185978 (nontriangular numbers as sums of (positive) triangular numbers). E.g., a(32)=231 is missing there because 231=A000217(21). See A185980.

%C For the numbers which are sums of two positive triangular numbers in exactly two ways see A064816.

%C The first number which can be written in exactly three ways as sums of positive triangular numbers is 81.

%C a(n) gives the positions where A052344 entries are >= 2: A052344(a(n)) >= 2.

%H T. D. Noe, <a href="/A185979/b185979.txt">Table of n, a(n) for n = 1..1000</a>

%e 16 = 15 + 1 = 10 + 6.

%e 81 = 45 + 36 = 66 + 15 = 78 + 3.

%e 231= 210 + 21 = 153 + 78

%Y Cf. A000217, A020756, A051533, A052344, A064816, A185980.

%K nonn,easy

%O 1,1

%A _Wolfdieter Lang_, Feb 15 2011