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 Nonn, easy, nice. (Posted on 2022-11-23)

To prove:

The sum of the first n even squares, less the sum of the first n squares, is equal to the nth square, plus the nth cube, plus the nth triangular number.

The sum of the first n odd squares, less the sum of the first n squares, is equal to the nth cube, less the nth triangular number.

 No Solution Yet Submitted by broll No Rating

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 computer exploration | Comment 3 of 5 |
sum1=0; sum2=0;tr=0;
for n=1:15
sum1=sum1+3*n^2;
tr=tr+n;
sum2=n^2+n^3+tr;
disp([sum1 sum2])
end
disp(' ')
sum1=0; sum2=0;tr=0;
for n=1:15
sum1=sum1+(2*n-1)^2-n^2;
tr=tr+n;
sum2= n^3-tr;
disp([sum1 sum2])
end

finds equal compares for both parts:

`>> nonnEasyNice     3     3    15    15    42    42    90    90   165   165   273   273   420   420   612   612   855   855  1155  1155          1518  1518        1950  1950        2457  2457        3045  3045        3720  3720            0     0     5     5    21    21    54    54   110   110   195   195   315   315   476   476   684   684   945   945  1265  1265  1650  1650  2106  2106  2639  2639  3255  3255`

They appear to be A059270 and A160378 in the OEIS, which describes each as nonn and easy.

 Posted by Charlie on 2022-11-23 11:20:15

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