A081219 One sixtieth the product of primitive Pythagorean triangles' sides whose odd values differ by 2.

1, 34, 259, 1092, 3333, 8294, 17927, 34952, 62985, 106666, 171787, 265420, 396045, 573678, 809999, 1118480, 1514513, 2015538, 2641171, 3413332, 4356373, 5497206, 6865431, 8493464, 10416665, 12673466, 15305499, 18357724, 21878557, 25919998

Offset: 1

Author

Lekraj Beedassy, Apr 18 2003

Keywords

• easy
• nonn

Comments

If Y and Z are 2-blocks of a (2n+1)-set X then a(n-2) is the number of 7-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 28 2007

Links

• Milan Janjic, Two Enumerative Functions
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A081752.

Programs

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{1,34,259,1092,3333,8294},30] (* Harvey P. Dale, Feb 11 2024 *)

PARI

Vec(x*(x^4+28*x^3+70*x^2+28*x+1)/(x-1)^6 + O(x^100)) \\ Colin Barker, Oct 06 2014

Formula

a(n) = n*(16*n^4 - 1)/15.

G.f.: x*(x^4+28*x^3+70*x^2+28*x+1) / (x-1)^6. - Colin Barker, Oct 06 2014

E.g.f.: exp(x)*x*(15 + 240*x + 400*x^2 + 160*x^3 + 16*x^4)/15. - Stefano Spezia, Aug 02 2025

Extensions

More terms from Ray Chandler, Oct 28 2003