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

1,2

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

Table of n, a(n) for n=1..30.

Index entries for sequences related to sums of squares

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007310, A097812, A001032.

Sequence in context: A174533 A174534 A295770 * A172222 A157369 A163434

Adjacent sequences: A151553 A151554 A151555 * A151557 A151558 A151559

Keyword

nonn,easy

Author

Michael David Hirschhorn, May 21 2009

Status

approved