A186656 -id:A186656 - cp's OEIS frontend

A186674 Total number of n-digit numbers requiring 14 positive biquadrates in their representation as sum of biquadrates.

0, 6, 60, 632, 6135, 60132, 600115, 6000118, 60000129, 600000127, 6000000136

Offset: 1

Martin Renner, Feb 25 2011

A102831(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + a(n) + A186676(n) + A186678(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A046045, A186673.

a(n) = A186673(n) - A186673(n-1).

a(5)-a(11) from Giovanni Resta, Apr 29 2016

A186676 Total number of n-digit numbers requiring 15 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 6, 60, 624, 6071, 60073, 600069, 6000069, 60000069, 600000061, 6000000071

Offset: 1

Martin Renner, Feb 25 2011

A102831(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + a(n) + A186678(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A046046, A186675.

a(n) = A186675(n) - A186675(n-1).

a(5)-a(11) from Giovanni Resta, Apr 29 2016

A186678 Total number of n-digit numbers requiring 16 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 4, 43, 241, 299, 287, 304, 309, 316, 286, 299

Offset: 1

Martin Renner, Feb 25 2011

A102831(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + a(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A046047, A186677.

a(n) = A186677(n) - A186677(n-1).

a(5)-a(11) from Giovanni Resta, Apr 29 2016

A186685 Total number of n-digit numbers requiring 19 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Martin Renner, Feb 25 2011

Eric Weisstein's World of Mathematics, Waring's Problem.
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A046050, A052268, A099591.

Cf. A161905, A186650, A186652, A186654, A186656, A186658, A186660(n) + A186662, A186664, A186666, A186668, A186670, A186672, A186674, A186676, A186678, A186681, A186683, A186684.

PadRight[{0, 1, 6}, 100] (* Paolo Xausa, Jul 26 2024 *)

a(n) = A186684(n) - A186684(n-1).
A161905(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + A186678(n) + A186681(n) + A186683(n) + a(n) = A052268(n).
a(n) = 0 for n >= 4. - Nathaniel Johnston, May 09 2011

A186650 Total number of n-digit numbers requiring 2 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

1, 4, 9, 29, 100, 317, 1007, 3146, 10016, 31712, 100204, 316799, 1002314, 3169309, 10022310, 31693094

Offset: 1

Martin Renner, Feb 25 2011

A102831(n) + a(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + A186678(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A003336, A186649.

isbiquadrate:=proc(n) type(root(n,4),posint); end:
isA003336:=proc(n) local x,y4; if isbiquadrate(n) then false; else for x from 1 do y4:=n-x^4; if y4A003336(k) then i:=i+1; fi; od: return(i); end: for n from 1 do print(a(n)); od;

a(n) = A186649(n)-A186649(n-1).

a(6) from Martin Renner, Feb 26 2011

a(7)-a(16) from Giovanni Resta, Apr 29 2016

A186652 Total number of n-digit numbers requiring 3 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

1, 5, 23, 112, 648, 3564, 19820, 110506, 622268, 3501263, 19699896

Offset: 1

Martin Renner, Feb 25 2011

A102831(n) + A186650(n) + a(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + A186678(n) + A186681(n) + A186683(n) + A186685(n) = A052268(n), for n>1.

Eric Weisstein's World of Mathematics, Waring's Problem.

Cf. A003337, A186651.

a(n) = A186651(n) - A186651(n-1).

a(5)-a(11) from Giovanni Resta, Apr 29 2016

A186681 Total number of n-digit numbers requiring 17 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 3, 30, 30, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Martin Renner, Feb 25 2011

A161905(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + A186678(n) + a(n) + A186683(n) + A186685(n) = A052268(n)

a(n) = 0 for n >= 6. - Nathaniel Johnston, May 09 2011

Eric Weisstein's World of Mathematics, Waring's Problem.
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A046048, A099591, A186683, A186685.

a(n) = A186680(n) - A186680(n-1).

A186683 Total number of n-digit numbers requiring 18 positive biquadrates in their representation as sum of biquadrates.

Original entry on oeis.org

0, 2, 17, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Martin Renner, Feb 25 2011

A161905(n) + A186650(n) + A186652(n) + A186654(n) + A186656(n) + A186658(n) + A186660(n) + A186662(n) + A186664(n) + A186666(n) + A186668(n) + A186670(n) + A186672(n) + A186674(n) + A186676(n) + A186678(n) + A186681(n) + a(n) + A186685(n) = A052268(n)

a(n) = 0 for n >= 5. - Nathaniel Johnston, May 09 2011

Eric Weisstein's World of Mathematics, Waring's Problem.
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A046049, A099591.

PadRight[{0, 2, 17, 5}, 100] (* Paolo Xausa, Jul 30 2024 *)

a(n) = A186682(n) - A186682(n-1).

cp's OEIS Frontend

A186674 Total number of n-digit numbers requiring 14 positive biquadrates in their representation as sum of biquadrates.

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A186676 Total number of n-digit numbers requiring 15 positive biquadrates in their representation as sum of biquadrates.

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A186678 Total number of n-digit numbers requiring 16 positive biquadrates in their representation as sum of biquadrates.

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A186685 Total number of n-digit numbers requiring 19 positive biquadrates in their representation as sum of biquadrates.

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A186650 Total number of n-digit numbers requiring 2 positive biquadrates in their representation as sum of biquadrates.

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A186652 Total number of n-digit numbers requiring 3 positive biquadrates in their representation as sum of biquadrates.

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A186681 Total number of n-digit numbers requiring 17 positive biquadrates in their representation as sum of biquadrates.

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A186683 Total number of n-digit numbers requiring 18 positive biquadrates in their representation as sum of biquadrates.

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