A037214 -id:A037214 - cp's OEIS frontend

A248807 Range of A037214 = coefficients of (sum_{n>0} n*X^(n^2))^2.

0, 1, 4, 6, 8, 9, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 38, 39, 40, 42, 48, 49, 50, 52, 54, 58, 60, 64, 68, 70, 72, 78, 80, 81, 88, 90, 96, 98, 102, 108, 110, 112, 118, 120, 121, 122, 128

Offset: 1

M. F. Hasler, Oct 14 2014

nonn

Also: Numbers of the form sum(xy ; x,y>0 and x^2+y^2=n) for some fixed n.

Cf. A037214.

A037215 Expansion of ( Sum_{k>=0} k*q^(k^2) )^3.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 6, 0, 0, 12, 0, 9, 8, 0, 36, 0, 0, 36, 12, 27, 0, 48, 54, 0, 48, 0, 72, 42, 0, 144, 60, 0, 0, 108, 108, 90, 96, 0, 198, 0, 0, 216, 120, 135, 72, 240, 108, 0, 64, 216, 360, 96, 0, 144, 396, 0, 288, 324, 0, 351, 0, 432, 432, 0, 0, 360, 492, 189, 288, 432, 540, 0, 96, 108, 648, 335, 216, 1008, 420, 0, 0, 852, 216, 657

Offset: 0

N. J. A. Sloane

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A037214, A037216, A037217.

More terms from Seiichi Manyama, Sep 14 2021

A037216 Expansion of ( Sum_{k>=0} k*q^(k^2) )^4.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 8, 0, 0, 24, 0, 12, 32, 0, 72, 16, 0, 144, 16, 54, 96, 96, 216, 0, 192, 216, 144, 256, 0, 576, 336, 0, 576, 336, 432, 261, 544, 864, 744, 384, 0, 1440, 672, 540, 1440, 960, 1296, 192, 1216, 1728, 1440, 1230, 864, 3168, 1416, 0, 1920, 3192, 2160, 2304, 2144, 1728, 3816, 256, 3456, 5328, 1568

Offset: 0

N. J. A. Sloane

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A037214, A037215, A037217.

More terms from Seiichi Manyama, Sep 14 2021

A037217 Expansion of ( Sum_{k>=0} k*q^(k^2) )^8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 16, 0, 0, 112, 0, 24, 448, 0, 336, 1120, 0, 2016, 1824, 252, 6720, 2240, 3024, 13440, 3712, 15120, 16800, 10768, 40320, 18816, 33600, 60480, 43392, 85792, 54432, 114030, 151872, 76608, 216768, 174336, 241920, 324240, 178304, 505008, 443520, 380800

Offset: 0

N. J. A. Sloane

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A037214, A037215, A037216.

More terms from Seiichi Manyama, Sep 14 2021

A347801 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^2.

Original entry on oeis.org

0, 0, 1, 0, 0, 8, 0, 0, 16, 0, 18, 0, 0, 72, 0, 0, 0, 32, 81, 0, 128, 0, 0, 0, 0, 288, 50, 0, 0, 200, 0, 0, 256, 0, 450, 0, 0, 72, 0, 0, 288, 800, 0, 0, 0, 648, 0, 0, 0, 0, 723, 0, 1152, 392, 0, 0, 0, 0, 882, 0, 0, 1800, 0, 0, 0, 1696, 0, 0, 512, 0, 0, 0, 1296, 1152, 2450, 0, 0, 0, 0, 0, 2048, 0, 162, 0, 0, 4176, 0, 0, 0, 3200, 1458

Offset: 0

Seiichi Manyama, Sep 14 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000404, A000925, A037214, A347802, A347803.

a(n) = sum(i=1, n, sum(j=1, n, (i^2+j^2==n)*(i*j)^2));

my(N=99, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, sqrtint(N), k^2*x^k^2)^2))

a(n) is sum of i^2 * j^2 for positive integers i,j such that i^2+j^2=n.

cp's OEIS Frontend

A248807 Range of A037214 = coefficients of (sum_{n>0} n*X^(n^2))^2.

Views

Author

Keywords

Comments

Crossrefs

A037215 Expansion of ( Sum_{k>=0} k*q^(k^2) )^3.

Views

Author

Keywords

Links

Crossrefs

Extensions

A037216 Expansion of ( Sum_{k>=0} k*q^(k^2) )^4.

Views

Author

Keywords

Links

Crossrefs

Extensions

A037217 Expansion of ( Sum_{k>=0} k*q^(k^2) )^8.

Views

Author

Keywords

Links

Crossrefs

Extensions

A347801 Expansion of ( Sum_{k>=0} k^2 * q^(k^2) )^2.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

PARI

Formula