A225258 -id:A225258 - cp's OEIS frontend

A225263 a(k) such that A225258 column k of T(n,k) = n*k^3 - a(k) for large n.

-1, 4, 18, 51, 91, 170, 249, 380, 520, 702, 882, 1171, 1378, 1710, 2057, 2447, 2795, 3297, 3690, 4306, 4808, 5449, 6049, 6906, 7479, 8268, 9115, 9993, 10812, 12000, 12792, 13936, 14925, 16106, 17308, 18753, 19745, 21203, 22615, 24258, 25475, 27235

Offset: 1

R. H. Hardin May 04 2013

sign

R. H. Hardin, Table of n, a(n) for n = 1..101

A225259 Number of distinct values of the sum of 2 products of three 0..n integers.

Original entry on oeis.org

3, 12, 36, 75, 157, 254, 434, 635, 911, 1237, 1734, 2162, 2908, 3611, 4461, 5435, 6734, 7879, 9568, 10964, 12861, 14913, 17438, 19426, 22381, 25251, 28482, 31624, 35879, 39100, 44165, 48267, 53463, 58590, 64476, 69214, 76693, 83132, 90303, 96766

Offset: 1

R. H. Hardin, May 04 2013

nonn

R. H. Hardin, Table of n, a(n) for n = 1..139

Row 2 of A225258.

def a(n):
  zn = list(range(n+1))
  prod3 = list(set(i*j*k for i in zn for j in zn[i:] for k in zn[j:]))
  return len(set(a+b for i, a in enumerate(prod3) for b in prod3[i:]))
print([a(n) for n in range(1, 42)]) # Michael S. Branicky, Mar 12 2021

A225260 Number of distinct values of the sum of 3 products of three 0..n integers.

Original entry on oeis.org

4, 20, 63, 141, 284, 478, 780, 1156, 1667, 2298, 3111, 4012, 5213, 6520, 8063, 9839, 11943, 14184, 16882, 19667, 22953, 26467, 30431, 34509, 39359, 44396, 49878, 55801, 62298, 68881, 76518, 84233, 92751, 101639, 111167, 121017, 132078, 143185, 155102

Offset: 1

R. H. Hardin May 04 2013

nonn

Row 3 of A225258

R. H. Hardin, Table of n, a(n) for n = 1..139

A225261 Number of distinct values of the sum of 4 products of three 0..n integers.

Original entry on oeis.org

5, 28, 90, 205, 409, 694, 1123, 1668, 2396, 3298, 4442, 5741, 7410, 9266, 11443, 13937, 16857, 20031, 23746, 27694, 32236, 37143, 42619, 48390, 55021, 62036, 69617, 77815, 86744, 96000, 106372, 117136, 128823, 141110, 154192, 167871, 182867, 198285

Offset: 1

R. H. Hardin, May 04 2013

nonn

R. H. Hardin, Table of n, a(n) for n = 1..138

Cf. A027426.

Row 4 of A225258.

from itertools import combinations_with_replacement as mc
def a(n):
  prods = set(a*b*c for a, b, c in mc(range(n+1), 3))
  return len(set(sum(p) for p in mc(prods, 4)))
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, May 28 2021

A225262 Number of distinct values of the sum of 5 products of three 0..n integers.

Original entry on oeis.org

6, 36, 117, 269, 534, 910, 1466, 2180, 3125, 4298, 5773, 7469, 9607, 12010, 14818, 18033, 21770, 25863, 30605, 35694, 41497, 47791, 54786, 62214, 70646, 79612, 89300, 99767, 111133, 123000, 136163, 149904, 164760, 180414, 197067, 214527, 233520

Offset: 1

R. H. Hardin May 04 2013

nonn

Row 5 of A225258

R. H. Hardin, Table of n, a(n) for n = 1..138

A225264 Minimum value unattainable as the sum of 2 attained values of abc with a,b,c 0..n integers.

Original entry on oeis.org

3, 7, 23, 23, 71, 71, 289, 311, 311, 311, 479, 479, 1559, 1559, 1559, 1559, 4253, 5637, 7142, 7469, 8843, 10103, 13445, 13445, 15457, 18043, 18191, 18191, 27313, 28442, 32249, 34637, 40367, 43445, 48409, 49957, 57167, 61459, 67513, 69241, 78913, 84533

Offset: 1

R. H. Hardin, May 04 2013

nonn

Related to A225258.

R. H. Hardin, Table of n, a(n) for n = 1..155

Cf. A225258.

A225265 Minimum value unattainable as the sum of 3 attained values of abc with a,b,c 0..n integers.

Original entry on oeis.org

4, 15, 50, 110, 222, 379, 632, 977, 1372, 1911, 2773, 3325, 4579, 5647, 6949, 8837, 10730, 12421, 15341, 17361, 20609, 23147, 27601, 30529, 35729, 39783, 45565, 50689, 56263, 62647, 70658, 76929, 83926, 93107, 102419, 110029, 122550, 131955, 145096

Offset: 1

R. H. Hardin May 04 2013

nonn

related to A225258

R. H. Hardin, Table of n, a(n) for n = 1..155

A225266 Minimum value unattainable as the sum of 4 attained values of abc with a,b,c 0..n integers.

Original entry on oeis.org

5, 23, 77, 174, 347, 595, 975, 1489, 2101, 2911, 4104, 5053, 6776, 8391, 10324, 12933, 15643, 18637, 22200, 25466, 30206, 34659, 39768, 44905, 51828, 58383, 65422, 73453, 81960, 89647, 100449, 111017, 121480, 134550, 146476, 158737, 173607, 188827

Offset: 1

R. H. Hardin May 04 2013

nonn

related to A225258

R. H. Hardin, Table of n, a(n) for n = 1..154

cp's OEIS Frontend

A225263 a(k) such that A225258 column k of T(n,k) = n*k^3 - a(k) for large n.

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A225259 Number of distinct values of the sum of 2 products of three 0..n integers.

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A225260 Number of distinct values of the sum of 3 products of three 0..n integers.

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A225261 Number of distinct values of the sum of 4 products of three 0..n integers.

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A225262 Number of distinct values of the sum of 5 products of three 0..n integers.

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A225264 Minimum value unattainable as the sum of 2 attained values of a*b*c with a,b,c 0..n integers.

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A225265 Minimum value unattainable as the sum of 3 attained values of a*b*c with a,b,c 0..n integers.

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A225266 Minimum value unattainable as the sum of 4 attained values of a*b*c with a,b,c 0..n integers.

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A225264 Minimum value unattainable as the sum of 2 attained values of abc with a,b,c 0..n integers.

A225265 Minimum value unattainable as the sum of 3 attained values of abc with a,b,c 0..n integers.

A225266 Minimum value unattainable as the sum of 4 attained values of abc with a,b,c 0..n integers.