A047672 Row 3 of square array defined in A047671.

1, 10, 37, 94, 193, 346, 565, 862, 1249, 1738, 2341, 3070, 3937, 4954, 6133, 7486, 9025, 10762, 12709, 14878, 17281, 19930, 22837, 26014, 29473, 33226, 37285, 41662, 46369, 51418, 56821, 62590, 68737, 75274, 82213, 89566, 97345, 105562, 114229, 123358, 132961

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

Links

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

Programs

Mathematica

lst={};Do[s0=n^3;s1=(n+1)^3;AppendTo[lst,(s1+s0)+n],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 19 2009 *)

PARI

vector(50, n, 2*n^3 - 3*n^2 + 4*n - 2) \\ Michel Marcus, Jan 07 2015

PARI

my(x='x+O('x^42)); Vec(x*(1+6*x+3*x^2+2*x^3)/(x-1)^4) \\ Elmo R. Oliveira, Aug 28 2025

Formula

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

From Elmo R. Oliveira, Aug 28 2025: (Start)

G.f.: x*(1 + 6*x + 3*x^2 + 2*x^3)/(1-x)^4.

E.g.f.: 2 + exp(x)*(-2 + 3*x + 3*x^2 + 2*x^3).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)

Extensions

More terms from Elmo R. Oliveira, Aug 28 2025