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

1,2

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

Table of n, a(n) for n=1..30.

Milan Janjic, Two Enumerative Functions

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A081752.

Sequence in context: A209951 A209944 A371403 * A254700 A241698 A159776

Adjacent sequences: A081216 A081217 A081218 * A081220 A081221 A081222

Keyword

easy,nonn

Author

Lekraj Beedassy, Apr 18 2003

Extensions

More terms from Ray Chandler, Oct 28 2003

Status

approved