A075681 a(n) = (n-1)*(n-2)^3 - A003878(n-3), with a(1) = a(2) = 0 and a(3) = 2.

0, 0, 2, 21, 60, 121, 207, 321, 466, 645, 861, 1117, 1416, 1761, 2155, 2601, 3102, 3661, 4281, 4965, 5716, 6537, 7431, 8401, 9450, 10581, 11797, 13101, 14496, 15985, 17571, 19257, 21046, 22941, 24945, 27061, 29292, 31641, 34111, 36705

Offset: 1

Author

Jon Perry, Oct 12 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A003878.

Programs

Magma

[0,0,2] cat [1/2*n^3+7/2*n^2-23*n+25: n in [4..50]]; // Vincenzo Librandi, Sep 07 2015

Maple

A075681:=n->1/2*n^3+7/2*n^2-23*n+25: (0,0,2,seq(A075681(n), n=4..50)); # Wesley Ivan Hurt, Sep 06 2015

Mathematica

CoefficientList[Series[x^2 (x^4 -x^3 -12 x^2 +13 x +2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 07 2015 *)
LinearRecurrence[{4,-6,4,-1}, {0,0,2,21,60,121,207}, 50] (* G. C. Greubel, Jan 03 2024 *)

SageMath

[(1/2)*(n^3+7*n^2-46*n+50) +(-1)^((n+2)//2)*binomial(5-n,2)*int(n<4) for n in range(1,51)] # G. C. Greubel, Jan 01 2024

Formula

From Ralf Stephan, Mar 13 2003: (Start)

a(n) = (1/2)*(n^3 + 7*n^2 - 46*n + 50), for n>3.

G.f.: x^3*(2 + 13*x - 12*x^2 - x^3 + x^4)/(1-x)^4. (End)

From G. C. Greubel, Jan 01 2024: (Start)

a(n) = (1/2)*(n^3 + 7*n^2 - 46*n + 50) + (-1)^floor((n+2)/2)*binomial(5 -n,2)*[n<4].

E.g.f.: (1/2)*(50 - 38*x + 10*x^2 + x^3)*exp(x) - 25 - 6*x + 3*x^2/2! + x^3/3!. (End)

Extensions

More terms from Ralf Stephan, Mar 13 2003