Sums of squares and sums of triangular numbers

2006 ◽  
pp. 55-84
Author(s):  
Bruce Berndt
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

On Sums of Triangular Numbers and Sums of Squares

1992 ◽  
Vol 99 (8) ◽  
pp. 752-757 ◽  
Author(s):  
John A. Ewell
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

Proofs of Some Conjectures of Z. -H. Sun on Relations Between Sums of Squares and Sums of Triangular Numbers

2020 ◽  
Vol 51 (1) ◽  
pp. 11-38
Author(s):  
Nayandeep Deka Baruah ◽  
Mandeep Kaur ◽  
Mingyu Kim ◽  
Byeong-Kweon Oh
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

Triangular Numbers and Sums of Squares

1988 ◽  
Vol 72 (462) ◽  
pp. 297
Author(s):  
C. J. Bradley
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

A GENERAL RELATION BETWEEN SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS

2005 ◽  
Vol 01 (02) ◽  
pp. 175-182 ◽  
Author(s):  
CHANDRASHEKAR ADIGA ◽  
SHAUN COOPER ◽  
JUNG HUN HAN
Keyword(s):  
Generating Functions ◽  
General Relation ◽  
The Other ◽  
Sums Of Squares ◽  
Triangular Numbers

Let rk(n) and tk(n) denote the number of representations of n as a sum of k squares, and as a sum of k triangular numbers, respectively. We give a generalization of the result rk(8n + k) = cktk(n), which holds for 1 ≤ k ≤ 7, where ck is a constant that depends only on k. Two proofs are provided. One involves generating functions and the other is combinatorial.

scholarly journals Mixed sums of squares and triangular numbers

2007 ◽  
Vol 127 (2) ◽  
pp. 103-113 ◽  
Author(s):  
Zhi-Wei Sun
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

On Sums of Triangular Numbers and Sums of Squares

1992 ◽  
Vol 99 (8) ◽  
pp. 752 ◽  
Author(s):  
John A. Ewell
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

scholarly journals SUMS OF SQUARES AND SUMS OF TRIANGULAR NUMBERS INDUCED BY PARTITIONS OF 8

2008 ◽  
Vol 04 (04) ◽  
pp. 525-538 ◽  
Author(s):  
NAYANDEEP DEKA BARUAH ◽  
SHAUN COOPER ◽  
MICHAEL HIRSCHHORN
Keyword(s):  
Sums Of Squares ◽  
Triangular Numbers

Let rk(n) and tk(n) denote the number of representations of an integer n as a sum of k squares, and as a sum of k triangular numbers, respectively. We prove that [Formula: see text] and therefore the study of the sequence t8(n) is reduced to the study of subsequences of r8(n). We give an additional 21 analogous results for sums of squares and sums of triangular numbers induced by partitions of 8. We give a brief indication of what happens for the case k ≥ 9.

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