Lorraine Lee - cp's OEIS frontend

User: Lorraine Lee

Lorraine Lee has authored 2 sequences.

A387220 Arithmetic mean of number of lattice points strictly inside circle of radius n centered on origin, and number of points not outside that circle.

3, 11, 27, 47, 75, 111, 147, 195, 251, 311, 375, 439, 523, 611, 703, 795, 895, 1007, 1127, 1251, 1371, 1515, 1651, 1791, 1951, 2115, 2287, 2451, 2623, 2815, 2999, 3207, 3407, 3619, 3847, 4051, 4287, 4511, 4771, 5019, 5255, 5523, 5787, 6075, 6355, 6623, 6919, 7211

Offset: 1

Lorraine Lee, Aug 22 2025

a(n) is the number of integer values (x, y) strictly inside the circle x^2+y^2=n^2, plus half the number of such lattice points that are part of the perimeter of that circle.

All terms are odd. - Chai Wah Wu, Aug 23 2025

			The unit circle has 1 lattice point strictly inside it and 5 lattice points not outside it. Halfway between 1 and 5 is 3, so a(1) = 3.

Average of A051132 and A000328.

a(n) = {4*n -1 + 2*sum(k=1, n-1, my(t=n^2-k^2); 2*sqrtint(t)-issquare(t))} \\ Andrew Howroyd, Aug 22 2025

from math import isqrt
def A387220(n): return 1+(sum(isqrt(m:=k*((n<<1)-k))+isqrt(m-1) for k in range(1,n+1))<<1) # Chai Wah Wu, Aug 23 2025

a(n) = (A051132(n) + A000328(n))/2.

a(n) = A256465(n^2). - R. J. Mathar, Aug 26 2025

A306385 a(n) is the maximum number of distinct distances possible between points in a hyperrectangular grid the sum of whose dimensions is n.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 12, 15, 18, 23, 28, 33, 40, 47, 56, 65, 74, 85, 98, 111, 127, 145, 163, 181, 199, 217, 238, 261, 284, 309, 338, 368, 398, 428, 458, 488, 518, 555, 592, 631, 673, 715, 757, 804, 852, 900, 948, 997, 1052, 1107, 1163, 1222, 1281, 1340, 1407, 1474, 1541, 1608, 1675

Offset: 1

Lorraine Lee, Feb 20 2019

nonn

Lorraine Lee, Ruby program which generates the sequence

b(v)={prod(k=1, #v, sum(i=0, v[k]-1, x^(i^2)))}
c(v)={sum(i=1, #v, v[i]<>0)}
a(n)={my(m=1); if(n>1, forpart(p=n, m=max(m, c(Vec(b(p)))), [2,n])); m} \\ Andrew Howroyd, Aug 11 2024

a(44)-a(45) from Lorraine Lee, Aug 11 2024

a(46) onwards from Andrew Howroyd, Aug 11 2024

cp's OEIS Frontend

User: Lorraine Lee

A387220 Arithmetic mean of number of lattice points strictly inside circle of radius n centered on origin, and number of points not outside that circle.

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