

A185978


Nontriangular numbers which are the sum of two (positive) triangular numbers.


3



2, 4, 7, 9, 11, 12, 13, 16, 18, 20, 22, 24, 25, 27, 29, 30, 31, 34, 37, 38, 39, 42, 43, 46, 48, 49, 51, 56, 57, 58, 60, 61, 64, 65, 67, 69, 70, 72, 73, 76, 79, 81, 83, 84, 87, 88, 90, 92, 93, 94, 97, 99, 100, 101, 102, 106, 108
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OFFSET

1,1


COMMENTS

This is A051533 (sums of two positive triangular numbers) excluding triangular numbers.
This is also A020756 (sums of two triangular numbers) excluding triangular numbers.
There may be multiple representations, e.g., 16 = 1 + 15 = 6 + 10.


LINKS



FORMULA

This is the sorted, made unique set {binomial(k+1,2) + binomial(L+1,2), 1 <= k <= L sufficiently large}, excluding members from A000217 (triangular numbers).


EXAMPLE

a(6) = 12 = 6 + 6,
a(17) = 31 = 3 + 28 = 10 + 21.


MATHEMATICA



CROSSREFS

Cf. A000217, A020756 (sums of two triangular numbers), A051533 (sums of two positive triangular numbers).


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



