login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309332 Number of ways the n-th triangular number T(n) = A000217(n) can be written as the sum of two positive triangular numbers. 3
0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 3, 0, 0, 1, 1, 3, 0, 0, 1, 0, 1, 0, 0, 3, 1, 1, 0, 1, 3, 0, 1, 1, 1, 2, 0, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 0, 3, 1, 1, 1, 0, 3, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 1, 5, 0, 1, 1, 0, 1, 0, 0, 3, 0, 3, 1, 0, 3, 1, 3, 1, 3, 3, 0, 1, 0, 0, 3, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,21

COMMENTS

The order doesn't matter. 21 = 6+15 = 15+6 are not counted as distinct solutions. - N. J. A. Sloane, Feb 22 2020

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000

FORMULA

a(n) > 0 <=> n in { A012132 }.

a(n) = 0 <=> n in { A027861 }.

a(n) = 1 <=> n in { A108769 }.

EXAMPLE

a(3) = 1: 2*3/2 + 2*3/2 = 3*4/2.

a(21) = 2: 6*7/2 + 20*21/2 = 12*13/2 + 17*18/2 = 21*22/2.

a(23) = 3: 9*10/2 + 21*22/2 = 11*12/2 + 20*21/2 = 14*15/2 + 18*19/2 = 23*24/2.

MAPLE

a:= proc(n) local h, j, r, w; h, r:= n*(n+1), 0;

      for j from n-1 by -1 do w:= j*(j+1);

        if 2*w<h then break fi;

        if issqr((h-w)*4+1) then r:=r+1 fi

      od; r

    end:

seq(a(n), n=1..120);

CROSSREFS

Cf. A000217, A001652, A012132, A027861, A046080 (the same for squares), A053141, A062301 (the same for primes), A108769, A309507.

Sequence in context: A285982 A261727 A234579 * A109362 A085246 A268726

Adjacent sequences:  A309329 A309330 A309331 * A309333 A309334 A309335

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 01 2019

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 11 01:51 EDT 2020. Contains 335600 sequences. (Running on oeis4.)