A075667 Sum of next n 6th powers.

1, 793, 66377, 1911234, 28504515, 271739011, 1874885963, 10136389172, 45311985069, 173957200405, 589679082421, 1802148522758, 5045944649967, 13108508706879, 31915866810295, 73427944186856, 160710828298553, 336507487921137, 677266380588289, 1315464522556810

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Formula

a(n) = Sum_{i=n(n-1)/2+1..n(n-1)/2+n} i^6.

a(n) = (21n^13 + 231n^11 + 693n^9 + 549n^7 - 126n^5 - 56n^3 + 32n)/1344. - Charles R Greathouse IV, Sep 17 2009

G.f.: x*(x^12 +779*x^11 +55366*x^10 +1053755*x^9 +7499895*x^8 +23228658*x^7 +33620292*x^6 +23228658*x^5 +7499895*x^4 +1053755*x^3 +55366*x^2 +779*x +1)/(x-1)^14. - Colin Barker, Jul 22 2012

Example

a(1) = 1^6 = 1; a(2) = 2^6 + 3^6 = 793; a(3) = 4^6 + 5^6 + 6^6 = 66377; a(4) = 7^6 + 8^6 + 9^6 + 10^6 = 1911234.

Mathematica

i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=6; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
With[{nn=20}, Total/@TakeList[Range[(nn(nn+1))/2]^6, Range[nn]]] (* or *) LinearRecurrence[{14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1}, {1, 793, 66377, 1911234, 28504515, 271739011, 1874885963, 10136389172, 45311985069, 173957200405, 589679082421, 1802148522758, 5045944649967, 13108508706879}, 20] (* Harvey P. Dale, Mar 29 2022 *)

Crossrefs

Cf. A001014 (6th powers).

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

Sequence in context: A130555 A133537 A213471 * A136543 A133274 A261657

Adjacent sequences: A075664 A075665 A075666 * A075668 A075669 A075670

Keyword

nonn,easy

Author

Zak Seidov, Sep 24 2002

Status

approved