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

Author

Zak Seidov, Mar 20 2009

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A048396 (sum of consecutive noncubes).

Programs

Mathematica

LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{139,5997,78414,553810,2677065,10009839,31098172,84004164,203427495},20] (* Harvey P. Dale, Nov 11 2024 *)

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

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.