A158527 Sum of squares of consecutive positive noncubes.

139, 5997, 78414, 553810, 2677065, 10009839, 31098172, 84004164, 203427495, 451263505, 931565514, 1811000022, 3346004389, 5917977555, 10077955320, 16602342664, 26561396547, 41402273589, 63048577990, 94018466010

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = (1/2)*n*(1 + n)*(1 + 9*n + 27*n^2 + 42*n^3 + 36*n^4 + 18*n^5 + 6*n^6).

G.f.: -x*(139*x^6+4746*x^5+29445*x^4+52300*x^3+29445*x^2+4746*x+139)/(x-1)^9.

Example

a(1) = 139 = 2^2+...+7^2, a(2) = 9^2+...+26^2.

Prog

(Python)
def A158527(n): return n*(n*(n*(n*(n*(n*(n*(6*(n + 4)) + 54) + 78) + 69) + 36) + 10) + 1)>>1 # Chai Wah Wu, Sep 03 2024

Crossrefs

Cf. A048396 (sum of consecutive noncubes).

Sequence in context: A217724 A230693 A223163 * A201174 A281249 A302089

Adjacent sequences: A158524 A158525 A158526 * A158528 A158529 A158530

Keyword

nonn,easy,changed

Author

Zak Seidov, Mar 20 2009

Status

approved