A374709 a(n) = n*(6*n^4 + 8*n^3 + 1 - (-1)^n)/16.

0, 1, 20, 132, 512, 1485, 3564, 7504, 14336, 25425, 42500, 67716, 103680, 153517, 220892, 310080, 425984, 574209, 761076, 993700, 1280000, 1628781, 2049740, 2553552, 3151872, 3857425, 4684004, 5646564, 6761216, 8045325, 9517500, 11197696, 13107200, 15268737, 17706452

Offset: 0

Author

Stefano Spezia, Jul 17 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -4, -4, 10, -4, -4, 4, -1).

Crossrefs

Row sums of A374708.

Cf. A000583, A016789, A229147.

Programs

Mathematica

LinearRecurrence[{4,-4,-4,10,-4,-4,4,-1},{0,1,20,132,512,1485,3564,7504},35]

Formula

O.g.f.: x*(1 + 16*x + 56*x^2 + 68*x^3 + 35*x^4 + 4*x^5)/((1 - x)^6*(1 + x)^2).

a(n) = 4*a(n-1) - 4*a(n-2) - 4*a(n-3) + 10*a(n-4) - 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - a(n-8) for n > 7.

E.g.f.: x*((8 + 73*x + 99*x^2 + 34*x^3 + 3*x^4)*cosh(x) + (7 + 73*x + 99*x^2 + 34*x^3 + 3*x^4)*sinh(x))/8.

a(2*n) = 4*A229147(n) = 4*A000583(n)*A016789(n).