A075668 Sum of next n 7th powers.

1, 2315, 374445, 17703664, 394340375, 5265954441, 48574262275, 338837482880, 1900477947429, 8950536157375, 36536761179281, 132397570996560, 433806511149115, 1303971065324669, 3637715990646375, 9507513902672896, 23461050872397545, 55013865421504275

Offset: 1

Author

Zak Seidov, Sep 24 2002

Keywords

• nonn
• easy

Examples

			a(1) = 1^7 = 1; a(2) = 2^7 + 3^7 = 2315; a(3) = 4^7 + 5^7 + 6^7 = 374445; a(4) = 7^7 + 8^7 + 9^7 + 10^7 = 17703664.
		

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Crossrefs

Cf. A001015 (7th powers).

Cf. A006003 (for natural numbers), A072474 (for squares), A075664 - A075671 (for 3rd to 10th powers), A069876 (n-th powers).

Programs

Mathematica

i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=7; Table[Sum[i^s, {i, i1, i2}], {n, 20}]

Formula

a(n) = Sum_{i=n*(n-1)/2+1..n*(n-1)/2+n} i^7.

a(n) = (3*n^15 + 42*n^13 + 168*n^11 + 206*n^9 - 11*n^7 - 56*n^5 + 32*n^3)/384. - Charles R Greathouse IV, Sep 17 2009

G.f.: x*(x^14 +2299*x^13 +337525*x^12 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +337525*x^2 +2299*x +1)/(x-1)^16. - Colin Barker, Jul 22 2012