A069473 First differences of (n+1)^6-n^6 (A022522).

62, 602, 2702, 8162, 19502, 39962, 73502, 124802, 199262, 303002, 442862, 626402, 861902, 1158362, 1525502, 1973762, 2514302, 3159002, 3920462, 4812002, 5847662, 7042202, 8411102, 9970562, 11737502, 13729562, 15965102, 18463202

Offset: 0

Author

Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 26 2002

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A001014, A022522, A069474, A069475, A069476, A068236.

Programs

Magma

[30*n^4+120*n^3+210*n^2+180*n+62: n in [0..30]]; // Bruno Berselli, Feb 25 2015

Mathematica

Differences[Table[(n + 1)^6 - n^6, {n, 0, 30}]] (* Harvey P. Dale, Dec 27 2011 *)

Formula

a(n) = 30*n^4 + 120*n^3 + 210*n^2 + 180*n + 62.

G.f.: 2*(31 + 146*x + 156*x^2 + 26*x^3 + x^4)/(1 - x)^5. [Bruno Berselli, Feb 25 2015]

Extensions

Offset changed from 1 to 0 and added a(0)=62 by Bruno Berselli, Feb 25 2015