A126335 a(n) = n*(4*n^2+5*n-3)/2.

3, 23, 72, 162, 305, 513, 798, 1172, 1647, 2235, 2948, 3798, 4797, 5957, 7290, 8808, 10523, 12447, 14592, 16970, 19593, 22473, 25622, 29052, 32775, 36803, 41148, 45822, 50837, 56205, 61938, 68048, 74547, 81447, 88760, 96498, 104673, 113297

Offset

1,1

Comments

Inner product of two arithmetic series (A016777, A005408): (1,4,7,...,3n-2)*(3,5,7,...,2n+1) = sum((3i-2)*(2i+1),i=1...n) = 1*3+4*3+7*7+...+(3n-2)*(2n+1) = (1/2)*n*(4*n^2+5*n-3).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(1)=3, a(2)=23, a(3)=72, a(4)=162; for n>4, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4).

G.f.: x*(3 + 11*x - 2*x^2)/(1 - x)^4.

Mathematica

CoefficientList[Series[(3 + 11 x - 2 x^2)/(1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 12 2013 *)

Prog

(PARI) a(n) = n*(4*n^2 + 5*n - 3)/2; \\ Michel Marcus, Oct 11 2013
(Magma) [n*(4*n^2+5*n-3)/2: n in [1..40]]; // Vincenzo Librandi, Oct 12 2013

Crossrefs

Sequence in context: A096207 A163210 A163211 * A256329 A196649 A363170

Adjacent sequences: A126332 A126333 A126334 * A126336 A126337 A126338

Keyword

nonn,easy

Author

Zak Seidov, Mar 11 2007

Status

approved