A371973 - OEIS

A371973

a(n) is the number of distinct areas > 0 of triangles with integer sides and perimeter n.

1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16, 13, 19, 14, 21, 19, 23, 20, 27, 23, 30, 27, 32, 29, 35, 32, 39, 34, 44, 39, 48, 43, 52, 47, 55, 51, 60, 53, 63, 59, 69, 58, 74, 67, 78, 73, 84, 75, 90, 81, 92, 88, 101, 91, 108, 93, 112, 106

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,5

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 3..10000

FORMULA

a(n) = |{A135622(k) : A070083(k) = n}| = |{A135622(k) : A026810(n) < k <= A026810(n+1)}|. - Peter Munn, Jul 29 2025

PROG

(PARI) A2(a, b, c) = {my (s=(a+b+c)/2); s*(s-a)*(s-b)*(s-c)};

a371973(n) = {my (A=List()); forpart (v=n, listput(A, A2(v[1], v[2], v[3])), [1, (n-1)\2], [3, 3]); #Set(A)};

(Python) def A371973(n): return len(set((2*(b+c)-n)*(n-2*b)*(n-2*c) for c in range((n+2)//3, (n+1)//2) for b in range((n-c+1)//2, c+1))) # David Radcliffe, Aug 01 2025

CROSSREFS

Cf. A005044, A007237, A024153, A317182, A371070.

See the formula section for the relationships with A026810, A070083, A135622 (which has many crossrefs related to areas of triangles).

Sequence in context: A029162 A325132 A225854 * A005044 A266755 A029142

Adjacent sequences: A371970 A371971 A371972 * A371974 A371975 A371976

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Apr 16 2024

EXTENSIONS

b-file corrected by David Radcliffe, Aug 01 2025

STATUS

approved