A094260 Sum of next n numbers/n if n divides the sum else n times the sum of next n numbers.

1, 10, 5, 136, 13, 666, 25, 2080, 41, 5050, 61, 10440, 85, 19306, 113, 32896, 145, 52650, 181, 80200, 221, 117370, 265, 166176, 313, 228826, 365, 307720, 421, 405450, 481, 524800, 545, 668746, 613, 840456, 685, 1043290, 761, 1280800, 841, 1556730, 925, 1875016, 1013, 2239786

Offset

1,2

Comments

Quasipolynomial of order 2 and degree 5. - Charles R Greathouse IV, Oct 14 2013

Links

Table of n, a(n) for n=1..46.

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,0,1).

Formula

For even n, a(n) = A000217(n^2) = n^2*(n^2+1)/2; for odd n, a(n) = (n^2 + 1)/2.

Sum_{n>=1} 1/a(n) = 1 + Pi^2/12 - Pi*cosech(Pi). - Amiram Eldar, Aug 23 2022

From Elmo R. Oliveira, May 05 2026: (Start)

a(n) = 5*a(n-2) - 10*a(n-4) + 10*a(n-6) - 5*a(n-8) + a(n-10) for n > 10.

G.f.: x*(1 + x^2)*(1 + 10*x - x^2 + 76*x^3 - x^4 + 10*x^5 + x^6)/(1 - x^2)^5. (End)

Example

The sequence is: 1/1, (2+3)*2, (4+5+6)/3, (7+8+9+10)*4, ...

Mathematica

LinearRecurrence[{0, 5, 0, -10, 0, 10, 0, -5, 0, 1}, {1, 10, 5, 136, 13, 666, 25, 2080, 41, 5050}, 50] (* Harvey P. Dale, May 01 2020 *)
(* Alternative: *)
fix[c_]:=If[Mod[Total[c], Length[c]]==0, Total[c]/Length[c], Length[c] Total[c]]; fix/@With[ {nn=50}, TakeList[ Range[(nn(nn+1))/2], Range[nn]]] (* Harvey P. Dale, Apr 05 2023 *)

Prog

(PARI) a(n) = if (n%2, (n^2+1)/2, n^2*(n^2+1)/2); \\ Michel Marcus, Aug 23 2022

Crossrefs

Cf. A000217, A001844, A037270.

Sequence in context: A096898 A146008 A038307 * A239603 A241439 A276348

Adjacent sequences: A094257 A094258 A094259 * A094261 A094262 A094263

Keyword

nonn,easy

Author

Amarnath Murthy, Apr 26 2004

Extensions

Edited and extended by Max Alekseyev, Apr 26 2009

Status

approved