A075690 a(n) = (n-1)*(n-2)^4 - A028294(n), for n > 4, with a(1) = a(2) = 0, a(3) = 2, and a(4) = 48.

0, 0, 2, 48, 304, 999, 2393, 4791, 8542, 14039, 21719, 32063, 45596, 62887, 84549, 111239, 143658, 182551, 228707, 282959, 346184, 419303, 503281, 599127, 707894, 830679, 968623, 1122911, 1294772, 1485479, 1696349, 1928743, 2184066, 2463767

Offset: 1

Author

Jon Perry, Oct 12 2002

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Ed Pegg Jr., Pancakes
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A028294.

Programs

Magma

[0,0,2,48] cat [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6: n in [4..50]]; // G. C. Greubel, Jan 03 2024

Mathematica

LinearRecurrence[{5,-10,10,-5,1}, {0,0,2,48,304,999,2393,4791,8542}, 50] (* G. C. Greubel, Jan 03 2024 *)

SageMath

[0,0,2,48] + [(11*n^4+19*n^3-632*n^2+2012*n-1686)/6 for n in range(4,51)] # G. C. Greubel, Jan 03 2024

Formula

From G. C. Greubel, Jan 03 2024: (Start)

a(n) = (n-1)*(n-2)^4 - A028294(n) + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].

a(n) = (11*n^4 + 19*n^3 - 632*n^2 + 2012*n - 1686)/6 + 46*[n=1] - 23*[n=2] - 9*[n=3] + [n=4].

G.f.: x^3*(2 + 38*x + 84*x^2 - 61*x^3 - 32*x^4 + 14*x^5 - x^6)/(1-x)^5.

E.g.f.: (1/6)*(-1686 + 1410*x - 498*x^2 + 85*x^3 + 11*x^4)*exp(x) + 281 + 46*x - 23*x^2/2 - 9*x^3/3! + x^4/4!. (End)

Extensions

More terms from David Wasserman, Jan 22 2005

Name clarified by G. C. Greubel, Jan 03 2024