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!)
A053603 Number of ways to write n as an ordered sum of two nonzero triangular numbers. 13
0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 2, 1, 2, 0, 0, 4, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 1, 4, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 3, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 2, 3, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 3, 2, 0, 0, 4, 0, 0, 2, 0, 6, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(A051611(n)) = 0; A051533(a(n)) > 0. - Reinhard Zumkeller, Jun 27 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: ( Sum_{k>=1} x^(k*(k+1)/2) )^2. - Ilya Gutkovskiy, Dec 24 2016

MATHEMATICA

nmax = 100; m0 = 10; A053603 := Table[a[n], {n, 0, nmax}]; Clear[counts]; counts[m_] := counts[m] = (Clear[a]; a[_] = 0; Do[k = i*(i+1)/2 + j*(j+1)/2; a[k] = a[k]+1, {i, 1, m}, {j, 1, m}]; A053603); counts[m = m0]; counts[m = 2*m]; While[ counts[m] != counts[m/2], m = 2*m]; A053603 (* Jean-Fran├žois Alcover, Sep 05 2013 *)

PROG

(Haskell)

a053603 n = sum $ map (a010054 . (n -)) $

                  takeWhile (< n) $ tail a000217_list

-- Reinhard Zumkeller, Jun 27 2013

(PARI)

istriang(n)={n>0 && issquare(8*n+1); }

a(n) = { my(t=1, ct=0, j=1); while (t<n, ct+=istriang(n-t); j+=1; t+=j; ); ct; }

\\ Joerg Arndt, Sep 05 2013

CROSSREFS

Cf. A000217, A007294, A051611, A051533, A052343-A052348, A053604.

Cf. A010054.

Sequence in context: A283310 A331534 A035445 * A085794 A336939 A239002

Adjacent sequences:  A053600 A053601 A053602 * A053604 A053605 A053606

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 20 2000

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 24 15:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)