A100503 Bisection of A000125.

1, 4, 15, 42, 93, 176, 299, 470, 697, 988, 1351, 1794, 2325, 2952, 3683, 4526, 5489, 6580, 7807, 9178, 10701, 12384, 14235, 16262, 18473, 20876, 23479, 26290, 29317, 32568, 36051, 39774, 43745, 47972, 52463, 57226, 62269, 67600, 73227, 79158

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = (4*n^3 + 5*n + 3)/3. - Ralf Stephan, May 15 2007

From Colin Barker, Aug 20 2012: (Start)

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

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

E.g.f.: (3 + 9*x + 12*x^2 + 4*x^3)*exp(x). - G. C. Greubel, Apr 03 2023

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {1, 4, 15, 42}, 40] (* Harvey P. Dale, Apr 12 2013 *)

Prog

(Magma) [(4*n^3+5*n+3)/3: n in [0..40]]; // G. C. Greubel, Apr 03 2023
(SageMath) [1+n*(4*n^2+5)/3 for n in range(41)] # G. C. Greubel, Apr 03 2023

Crossrefs

Cf. A000125.

Sequence in context: A342352 A011844 A075468 * A085829 A085567 A187928

Adjacent sequences: A100500 A100501 A100502 * A100504 A100505 A100506

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 24 2004

Extensions

More terms from Hugo Pfoertner, Nov 25 2004

Status

approved