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

Author

N. J. A. Sloane, Nov 24 2004

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000125.

Programs

Magma

[(4*n^3+5*n+3)/3: n in [0..40]]; // G. C. Greubel, Apr 03 2023

Mathematica

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

SageMath

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

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

Extensions

More terms from Hugo Pfoertner, Nov 25 2004