A345665 -id:A345665 - cp's OEIS frontend

A351696 a(n) is the numerator of the squared circumradius of a cyclic quadrilateral with sides n, n+1, n+2, n+3.

385, 3289, 1729, 53041, 146329, 38665, 741169, 1449721, 294409, 4582249, 7568185, 1335961, 18477481, 27589921, 4463641, 57210985, 79885729, 12177649, 147998761, 197007889, 28761265, 336087409, 431638801, 60980689, 691402609, 863589385, 118901521, 1316247361, 1607847241

Offset: 1

Hugo Pfoertner, Feb 26 2022

			385/96, 3289/480, 1729/160, 53041/3360, 146329/6720, 38665/1344, ...

Wikipedia, Cyclic quadrilateral, Parameshvara's circumradius formula.

32*A351697(n) are the corresponding denominators.

Cf. A000332, A345665, A351698.

a(n) = numerator((2*n^6 + 18*n^5 + 65*n^4 + 120*n^3 + 117*n^2 + 54*n + 9)/(n^4 + 6*n^3 + 11*n^2 + 6*n)).

a(n) = 24*A351698(n) + 1.

A351697 32*a(n) is the denominator of the squared circumradius of a cyclic quadrilateral with sides n, n+1, n+2, n+3.

Original entry on oeis.org

3, 15, 5, 105, 210, 42, 630, 990, 165, 2145, 3003, 455, 5460, 7140, 1020, 11628, 14535, 1995, 21945, 26565, 3542, 37950, 44850, 5850, 61425, 71253, 9135, 94395, 107880, 13640, 139128, 157080, 19635, 198135, 221445, 27417, 274170, 303810, 37310, 370230, 407253, 49665

Offset: 1

Hugo Pfoertner, Feb 26 2022

			(1/32)*{385/3, 3289/15, 1729/5, 53041/105, 146329/210, 38665/42, ...}

A351696 gives the corresponding numerators.

Cf. A000332, A052762, A345665, A351698.

a(n) = denominator(b(n)), where b(n) = (8*(2*n^6 + 18*n^5 + 65*n^4 + 120*n^3 + 117*n^2 + 54*n + 9))/(n^4 + 6*n^3 + 11*n^2 + 6*n).

cp's OEIS Frontend

A351696 a(n) is the numerator of the squared circumradius of a cyclic quadrilateral with sides n, n+1, n+2, n+3.

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