A151556 Values of (n^5+47*n)/48 as n ranges over the numbers that are == +-1 mod 6.

1, 70, 357, 3366, 7748, 29597, 51604, 134113, 203475, 427344, 596471, 1094240, 1444702, 2413711, 3062718, 4778067, 5884949, 8712458, 10485145, 14894314, 17595816, 24172785, 28127672, 37588181, 43189063, 56391412, 64105419, 82063428, 92438690, 116334659

Offset: 1

Author

Michael David Hirschhorn, May 21 2009

Keywords

• nonn
• easy

Comments

((n^5+47n)/48)^2 is the sum of the squares of the n^2 integers from (n^4-24n^2-25)/48 to (n^4+24n^2-73)/48. For example, when n=5, 70^2 is the sum of the 25 squares of the integers from 0 to 24.

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A007310, A097812, A001032.

Programs

Magma

[((2*n-1)*(81*n^4-162*n^3+144*n^2-63*n+58)+(135*n^4-270*n^3+210*n^2-75*n+26)*(-1)^n)/32: n in [1..30]]; // Vincenzo Librandi, Oct 25 2014

Mathematica

With[{nn=20},(#^5+47#)/48&/@Sort[Join[6Range[0,nn]+1,6Range[nn]-1]]] (* Harvey P. Dale, Nov 15 2011 *)

Formula

a(n) = a(n-1)+5*a(n-2)-5*a(n-3)-10*a(n-4)+10*a(n-5)+10*a(n-6)-10*a(n-7)-5*a(n-8)+5*a(n-9)+a(n-10)-a(n-11). [R. J. Mathar, May 21 2009]

G.f.: x*(1 +69*x +282*x^2 +2664*x^3 +2957*x^4 +7494*x^5 +2957*x^6 +2664*x^7 +282*x^8 +69*x^9 +x^10)/((1+x)^5*(x-1)^6). [R. J. Mathar, May 21 2009]

a(n) = ((2*n-1)*(81*n^4-162*n^3+144*n^2-63*n+58)+(135*n^4-270*n^3+210*n^2-75*n+26)*(-1)^n)/32. - Tani Akinari, Oct 25 2014