A133767 a(n) = (4*n+3)*(4*n+5)*(4*n+7).

105, 693, 2145, 4845, 9177, 15525, 24273, 35805, 50505, 68757, 90945, 117453, 148665, 184965, 226737, 274365, 328233, 388725, 456225, 531117, 613785, 704613, 803985, 912285, 1029897, 1157205, 1294593, 1442445, 1601145, 1771077, 1952625, 2146173, 2352105, 2570805, 2802657

Offset: 0

Author

Miklos Kristof, Jan 02 2008

Keywords

• nonn
• easy
• changed

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Maple

seq((4*n+3)*(4*n+5)*(4*n+7),n=0..40);

Mathematica

a[n_]:=(4*n+3)*(4*n+5)*(4*n+7); Array[a,35,0] (* Stefano Spezia, Aug 27 2025 *)

Formula

G.f.: 3*(35 + 91*x + x^2 + x^3)/(1-x)^4.

E.g.f: (105 + 588*x + 432*x^2 + 64*x^3)*exp(x).

Sum_{m>0} 4/a(m) = 5/6 - Pi/4.

Extensions

a(31)-a(34) from Stefano Spezia, Aug 27 2025