cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A341774 Number of partitions of n into 3 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 0, 0, 2
Offset: 3

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A063993, A068980, A341775, A341776, A341777, A341778.

A341775 Number of partitions of n into 4 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 0, 2, 2, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 1, 2, 2, 0, 0, 2, 1, 1, 2, 0, 0, 3, 1, 0, 2, 1, 1
Offset: 4

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A068980, A319814, A341774, A341776, A341777, A341778.

A341776 Number of partitions of n into 5 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 1, 0, 1, 1, 0, 2, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 1, 1, 2, 1, 0, 3, 1, 1, 3, 2, 0, 2, 1, 0, 2, 2, 0, 3, 2, 1, 2, 2, 1, 2, 2, 1, 3, 2, 1, 2, 2, 1, 2, 2, 1, 2, 3, 2, 2, 3, 1, 2, 3, 1, 1, 4, 1, 2, 3, 1, 0, 4, 2
Offset: 5

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A068980, A319815, A341774, A341775, A341777, A341778.

A341777 Number of partitions of n into 6 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 2, 1, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 1, 3, 0, 2, 3, 1, 1, 3, 1, 1, 3, 1, 1, 4, 2, 1, 3, 2, 0, 3, 2, 1, 4, 3, 1, 3, 2, 1, 3, 3, 1, 4, 3, 2, 3, 3, 1, 3, 3, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 5, 2, 2, 5, 2, 2, 5, 2, 2, 6, 3, 3
Offset: 6

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A068980, A319816, A341774, A341775, A341776, A341778.

A341806 Number of ways to write n as an ordered sum of 7 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 7, 0, 0, 21, 0, 0, 42, 0, 0, 77, 0, 0, 126, 0, 0, 168, 7, 0, 211, 42, 0, 252, 105, 0, 252, 182, 0, 245, 315, 0, 231, 469, 0, 175, 574, 21, 140, 735, 105, 105, 854, 210, 56, 875, 315, 42, 987, 525, 21, 952, 693, 7, 882, 840, 42, 924, 1155, 140, 770, 1260, 211, 749, 1470
Offset: 7

Views

Author

Ilya Gutkovskiy, Feb 20 2021

Keywords

Links

Crossrefs

Cf. A000292, A023533, A023670, A282582, A340952, A341778, A341794, A341795, A341796, A341797, A341807, A341808, A341809.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (&+[x^Binomial(j+2,3): j in [1..20]])^7 )); // G. C. Greubel, Jul 19 2022
  • Mathematica
    nmax = 72; CoefficientList[Series[Sum[x^Binomial[k + 2, 3], {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &
  • SageMath
    def f(m, x): return ( sum( x^(binomial(j+2,3)) for j in (1..20) ) )^m
def A341806_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(7, x) ).list()
a=A341806_list(100); a[7:81] # G. C. Greubel, Jul 19 2022

Formula

G.f.: ( Sum_{k>=1} x^binomial(k+2,3) )^7.

A341791 Number of partitions of n into 8 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 3, 2, 0, 3, 2, 0, 2, 3, 0, 3, 4, 1, 2, 4, 1, 2, 4, 1, 2, 5, 2, 2, 4, 2, 1, 5, 3, 2, 6, 4, 2, 5, 3, 2, 5, 4, 2, 6, 4, 3, 5, 5, 2, 5, 5, 4, 6, 6, 3, 6, 6, 3, 5, 6, 3, 6, 8, 4, 5, 8, 4, 5, 8, 4, 5, 10
Offset: 8

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A068980, A319818, A341774, A341775, A341776, A341777, A341778, A341792, A341793.

A341792 Number of partitions of n into 9 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 0, 3, 2, 0, 3, 3, 0, 3, 4, 1, 3, 4, 1, 2, 5, 1, 3, 5, 2, 2, 5, 2, 2, 5, 3, 2, 7, 4, 3, 6, 4, 2, 6, 4, 3, 7, 5, 3, 6, 5, 3, 6, 6, 4, 7, 7, 5, 7, 7, 3, 7, 7, 5, 7, 9, 4, 7, 9, 5, 6, 10, 5, 8
Offset: 9

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A068980, A319819, A341774, A341775, A341776, A341777, A341778, A341791, A341793.

A341793 Number of partitions of n into 10 nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 0, 4, 2, 0, 3, 3, 0, 4, 4, 1, 3, 4, 1, 3, 5, 1, 3, 6, 2, 3, 5, 2, 2, 6, 3, 3, 7, 4, 3, 7, 4, 3, 7, 5, 3, 8, 5, 4, 7, 6, 3, 7, 6, 5, 8, 8, 5, 8, 8, 5, 8, 8, 5, 9, 10, 6, 8, 10, 5, 8, 11, 7
Offset: 10

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Crossrefs

Cf. A000292, A023533, A024692, A068980, A319820, A341774, A341775, A341776, A341777, A341778, A341791, A341792.

A341773 Number of partitions of 2*n into exactly n nonzero tetrahedral numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 3, 1, 0, 3, 1, 0, 3, 1, 0, 4, 2, 0, 4, 2, 0, 4, 3, 0, 5, 4, 1, 5, 4, 1, 5, 5, 1, 6, 6, 2, 6, 6, 2, 6, 7, 3, 7, 9, 4, 8, 9, 4, 8, 10, 5, 9, 12, 6, 10, 12, 7, 10, 13, 8, 12, 15, 10, 13, 16, 11, 13, 17, 12
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

Links

Crossrefs

Cf. A000292, A024692, A062748, A068980, A298269, A319799, A338586, A341774, A341775, A341776, A341777, A341778.

Programs

  • Mathematica
    nmax = 80; CoefficientList[Series[Product[1/(1 - x^(Binomial[k + 4, 3] - 1)), {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=0} 1 / (1 - x^(binomial(k+4,3)-1)).
Showing 1-9 of 9 results.

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