A154560 a(n) = (n+3)^2*n/2 + 1.

1, 9, 26, 55, 99, 161, 244, 351, 485, 649, 846, 1079, 1351, 1665, 2024, 2431, 2889, 3401, 3970, 4599, 5291, 6049, 6876, 7775, 8749, 9801, 10934, 12151, 13455, 14849, 16336, 17919, 19601, 21385, 23274, 25271, 27379, 29601, 31940, 34399, 36981

Offset: 0

Author

Klaus Brockhaus, Jan 12 2009

Keywords

• nonn
• easy

Comments

8*a(n) is the y value of a solution (x, y) to the Diophantine equation 2*x^3+12*x^2 = y^2. The corresponding x value is A152811(n+1).

Examples

			a(5) = (5+3)^2*5/2+1 = 64*5/2+1 = 161.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A058794 (row 3 of A007754), A117560 (n*(n^2-1)/2-1), A144129 (4*n^3-3*n), A141530, A152811 (2*(n^2+2*n-2)).

Programs

Magma

[(n+3)^2*n/2 + 1: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

PARI

{for(n=0,40,print1((n+3)^2*n/2+1,","))}

Formula

G.f.: (1+5*x-4*x^2+x^3)/(1-x)^4.

a(n) = A058794(n)/2.

a(n) = A117560(n+2) - n - 1.

a(2*n) = A144129(n+1).

a(2*n-1) = A141530(n+1). a(n) = -a(-n-4). - Bruno Berselli, Sep 05 2011

a(n) = ((n+2-i)^3+(n+2+i)^3)/4, where i is the imaginary unit. - Nicolas Bělohoubek, Jul 03 2025