A215147 For n odd, a(n) = 1^2+2^2+3^2+...+n^2; for n even, a(n) = (1^2+2^2+3^2+...+n^2)+1.

1, 2, 5, 6, 14, 15, 30, 31, 55, 56, 91, 92, 140, 141, 204, 205, 285, 286, 385, 386, 506, 507, 650, 651, 819, 820, 1015, 1016, 1240, 1241, 1496, 1497, 1785, 1786, 2109, 2110, 2470, 2471, 2870, 2871, 3311, 3312, 3795, 3796, 4324, 4325, 4900, 4901, 5525, 5526

Offset: 1

Author

Kritsana Sokhuma, Aug 04 2012

Keywords

• nonn
• easy

Comments

Square pyramidal numbers when n is odd.

An interleaving of A000330 and A056520. - Michel Marcus, Aug 07 2013

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Crossrefs

Cf. A000330, A056520.

Programs

Maple

for i from 1 to 100 do a(2*i-1):=sum('k^2','k'=1..i);
a(2*i):=a(2*i-1)+1; end do;

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 2, 5, 6, 14, 15, 30}, 50] (* or *)
Riffle[#, #+1] & [Accumulate[Range[25]^2]] (* Paolo Xausa, Feb 22 2024 *)

Formula

From Colin Barker, Nov 16 2012: (Start)

a(n) = (6*(5+3*(-1)^n)+(13-9*(-1)^n)*n-3*(-3+(-1)^n)*n^2+2*n^3)/48.

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

Extensions

More terms from Paolo Xausa, Feb 22 2024