login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A302996 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals: A(n,k) = [x^(n^2)] theta_3(x)^k, where theta_3() is the Jacobi theta function. 2
1, 1, 0, 1, 2, 0, 1, 4, 2, 0, 1, 6, 4, 2, 0, 1, 8, 6, 4, 2, 0, 1, 10, 24, 30, 4, 2, 0, 1, 12, 90, 104, 6, 12, 2, 0, 1, 14, 252, 250, 24, 30, 4, 2, 0, 1, 16, 574, 876, 730, 248, 30, 4, 2, 0, 1, 18, 1136, 3542, 4092, 1210, 312, 54, 4, 2, 0, 1, 20, 2034, 12112, 18494, 7812, 2250, 456, 6, 4, 2, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A(n,k) is the number of ordered ways of writing n^2 as a sum of k squares.

LINKS

Table of n, a(n) for n=0..77.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to sums of squares

FORMULA

A(n,k) = [x^(n^2)] (Sum_{j=-infinity..infinity} x^(j^2))^k.

EXAMPLE

Square array begins:

1,  1,   1,   1,    1,     1,  ...

0,  2,   4,   6,    8,    10,  ...

0,  2,   4,   6,   24,    90,  ...

0,  2,   4,  30,  104,   250,  ...

0,  2,   4,   6,   24,   730,  ...

0,  2,  12,  30,  248,  1210,  ...

MATHEMATICA

Table[Function[k, SeriesCoefficient[EllipticTheta[3, 0, x]^k, {x, 0, n^2}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten

Table[Function[k, SeriesCoefficient[Sum[x^i^2, {i, -n, n}]^k, {x, 0, n^2}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten

CROSSREFS

Columns k=0..4 give A000007, A040000, A046109, A016725, A267326.

Main diagonal gives A232173.

Cf. A000122, A122141, A255212, A286815.

Sequence in context: A228924 A246862 A194686 * A266213 A289522 A316273

Adjacent sequences:  A302993 A302994 A302995 * A302997 A302998 A302999

KEYWORD

nonn,tabl

AUTHOR

Ilya Gutkovskiy, Apr 17 2018

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)