A337173 a(n) = Sum_{k=1..floor(n/2)} k^2 * (n-k)^2.

0, 1, 4, 25, 52, 170, 280, 674, 984, 1979, 2684, 4795, 6188, 10164, 12656, 19524, 23664, 34773, 41268, 58333, 68068, 93214, 107272, 143078, 162760, 212303, 239148, 306047, 341852, 430312, 477152, 592008, 652256, 799017, 875364, 1060257, 1155732, 1385746, 1503736

Offset

1,3

Links

Table of n, a(n) for n=1..39.

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

Formula

G.f.: x^2*(1+3*x+16*x^2+12*x^3+23*x^4+5*x^5+4*x^6)/((1-x)^6*(1+x)^5).

a(n) = (2*n-1+(-1)^n)*(2*n+3+(-1)^n)*(16*n^3-n^2+10*n-4-(n^2+6*n+4)*(-1)^n)/3840.

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).

Example

a(6) = 1^2*5^2 + 2^2*4^2 + 3^2*3^2 = 25 + 64 + 81 = 170.

Mathematica

CoefficientList[Series[x (1 + 3 x + 16 x^2 + 12 x^3 + 23 x^4 + 5 x^5 + 4 x^6)/((1 - x)^6 (1 + x)^5), {x, 0, 80}], x]

Crossrefs

Cf. A023855.

Sequence in context: A199772 A245697 A089767 * A135784 A131069 A016790

Adjacent sequences: A337170 A337171 A337172 * A337174 A337175 A337176

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 28 2021

Status

approved