A269232 a(n) = (n + 1)*(6*n^2 + 15*n + 4)/2.

2, 25, 87, 206, 400, 687, 1085, 1612, 2286, 3125, 4147, 5370, 6812, 8491, 10425, 12632, 15130, 17937, 21071, 24550, 28392, 32615, 37237, 42276, 47750, 53677, 60075, 66962, 74356, 82275, 90737, 99760, 109362, 119561, 130375, 141822, 153920, 166687, 180141

Offset: 0

Author

Ilya Gutkovskiy, Feb 20 2016

Keywords

• nonn
• easy

Examples

			a(0) = 0 + 1*2 = 2;
a(1) = 0 + 1*2 + 3 + 4*5 = 25;
a(2) = 0 + 1*2 + 3 + 4*5 + 6 + 7*8 = 87;
a(3) = 0 + 1*2 + 3 + 4*5 + 6 + 7*8 + 9 + 10*11 = 206;
a(4) = 0 + 1*2 + 3 + 4*5 + 6 + 7*8 + 9 + 10*11 + 12 + 13*14 = 400, etc.
		

Links

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

Crossrefs

Cf. A001477, A001504, A008585.

Programs

Magma

[(n+1)*(6*n^2+15*n+4)/2: n in [0..40]]; // Vincenzo Librandi, Feb 22 2016

Mathematica

Table[(n + 1) ((6 n^2 + 15 n + 4)/2), {n, 0, 38}]
Table[Sum[3 k + (3 k + 1) (3 k + 2), {k, 0, n}], {n, 0, 38}]
LinearRecurrence[{4, -6, 4, -1}, {2, 25, 87, 206}, 39]

PARI

Vec((2 + 17*x - x^2)/(x - 1)^4 + O(x^50)) \\ Michel Marcus, Feb 22 2016

Formula

G.f.: (2 + 17*x - x^2)/(x - 1)^4.

a(n) = Sum_{k=0..n} (3*k + (3*k+1)*(3*k+2)) = Sum_{k=0..n} (A008585(k) + A001504(k)).

Sum_{n>=0} 1/a(n) = 0.56407113696623548787861365289...